There
to this
equation representing the number of seconds
elapsed between the dolphin exiting and
reentering the water.​

N equals 78

The equation: (56+n)/2 - 40=27

Add 40 to 27=67

Multiply everything by 2 leaving you with 56+n=134

Subtract 56 from 134

Leaves you with n=78

If you plug it in you would get 67-40, which equals 27

Final answer:

The rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec. The rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.

Explanation:

To solve for the rates at which the tip of the shadow is moving away from the pole and from the person, we can use similar triangles and related rates. Let's solve each part step by step:

a. Rate the tip of the shadow is moving away from the pole:

We have a right triangle formed by the pole, the person, and the tip of the shadow. Let x be the distance between the person and the tip of the shadow.

Since the person is moving away from the pole at a rate of 2 ft/sec, dx/dt = 2 ft/sec.

Using the similar triangles, we have:

(12 ft + 5.5 ft) / x = 12 ft / (x + 25 ft)

Simplifying the equation gives:

17.5x + 437.5 = 12x + 300

5.5x = 137.5

x = 25 ft

Now, let's differentiate both sides of the equation with respect to time t:

17.5 (dx/dt) = 12 (dx/dt) + 0

17.5 (dx/dt) - 12 (dx/dt) = 0

5.5 (dx/dt) = 0

dx/dt = 0 ft/sec

So, the rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec.

b. Rate the tip of the shadow is moving away from the person:

Using the similar triangles, we have:

(12 ft + 5.5 ft) / x = 5.5 ft / 25 ft

Simplifying the equation gives:

17.5x = 137.5

x = 7.857 ft

Now, let's differentiate both sides of the equation with respect to time t:

17.5 (dx/dt) = 5.5 (dx/dt) + d(7.857)/dt

12 (dx/dt) = d(7.857)/dt

dx/dt = (d(7.857)/dt) / 12

dx/dt = (0 ft/sec) / 12

So, the rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.

Answer:

I'm newbie here

Step-by-step explanation:

Elimination Method.

4x + 6/y = 15 → step 1

6x - 8/y = 14 → step 2

so,

4x + 6/y = 15 |×6|

6x - 8/y = 14 |×4|

24x + 6/y(6) = 90

24x - 8/y(4) = 56

24x + 36/y = 90

24x - 32/y = 56

____________ _

68/y = 34

68 = 34y

34y = 68

y = 2

subsitution y = 2 to..

4x + 6/y = 15

4x + 6/2 = 15

4x + 3 = 15

4x = 12

x = 3

So, for x is 3, and for y is 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Multiply equation 1 by -6

-24x - 36/y = -90

Multiply equation 2 by 4

24x - 32/y = 56

Add the two equations:

-36/y - 32/y = -34

-68/y = -34

y = -68/-34

y = 2

4x + 6/2 = 15

4x = 15 - 3

4x = 12

x = 3

Given Information:

Coastline of Canada = 202080 km

Coastline of British Columbia = 2/15 of Coastline of Canada

Required Information:

How long is the coastline of British Columbia = ?

Answer:

Coastline of British Columbia is 26944 km long

Step-by-step explanation:

We are given the length of Coastline of Canada that is 202080 km

We also know that Coastline of British Columbia is 2/15 of the Coastline of Canada.

So,

Coastline of British Columbia = (2/15)*202080

Coastline of British Columbia = 26944 km

Therefore, the Coastline of British Columbia is about 26944 km.

Answer:

5

Step-by-step explanation:

To find the slope given two points, we use the formula

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

   = (-13-2)/(-2 -1)

   = -15/-3

   =5

Answer:

The slope is 5

Step-by-step explanation:

Δ means the change in

slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5

Slope = 5

Answer:

He use 120 grams of flour.

Step-by-step explanation:

Given:

Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat.

Now, to find the weight of flour he use in making flaky pastry.

Let the weight of flour be [tex]x.[/tex]

Weight of fat = 90 grams.

The ratio of flour and fat used in making flaky pastry is 4 : 3.

As, 4 is equivalent to 3.

Thus, [tex]x[/tex] is equivalent to 90.

Now, to solve using cross multiplication method:

[tex]\frac{4}{3} =\frac{x}{90} \\\\By\ cross\ multiplying\ we\ get:\\\\360=3x\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\120=x\\\\x=120\ grams.[/tex]

Therefore, he use 120 grams of flour.

Answer:

The answer to your question is 5.7

Step-by-step explanation:

Data

Point A = (2, 3)

Point B = (-2, 7)

Process

To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.

Formula

dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]

-Identify wich is the value of x1, y1, x2, y2

        x1 = 2   y1 = 3  x2 = -2  y2 = 7

-Substittion

dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]

-Simplification

dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]

dAB = [tex]\sqrt{16 + 16}[/tex]

dAB = [tex]\sqrt{32}[/tex]

-Result

dAB = 5.65 ≈ 5.7

Answer:

[tex]cos(G)=\frac{28}{53}[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle EFG

[tex]cos(G)=\frac{GF}{EG}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(G)=\frac{28}{53}[/tex]

Answer:714.1

Step-by-step explanation:

500 times tan(55)

We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.

So tangent(55°) = depth / 500 meters.

To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).

Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.

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Answer:

360 combinations

Step-by-step explanation:

To calculate the number of different combinations of 2 different flavors, 1 topping, and 1 cone, we are going to use the rule of multiplication as:

              6          *        5             *            4           *          3             = 360

       1st flavor           2nd flavor              topping              cone

Because first, we have 6 possible options for the flavor, then we only have 5 possible options for the 2nd flavor. Then, we have 4 options for the topping and finally, we have 3 options for the cone.

It means that there are 360 different combinations of two different flavors, one topping, and one cone are possible

Answer:

[tex]\frac{3}{50}[/tex]

Step-by-step explanation:

Answer: 6/10

Step-by-step explanation:

the 6 is in the tenth place which means it is by ten

Answer: A) organized in similar manner adjacent to each other, and are anatomically similar from one person to the next.

The physical organization of the motor cortex and somatosensory cortex, which are located next to one another, is the same in every individual. Hence, Option A is correct.

The brain's cerebral cortex is located on the outside. It looks wrinkled because of the numerous folds on its surface. Numerous deep grooves, or sulci, and elevated regions, or gyri, make up the folds.

These folds increase the surface area of the cerebral cortex, which enables more nerve cells to handle significant amounts of information. A nerve cell's dendrites are the area where a chemical communication from another cell is received. The mass of the brain is roughly divided in half by the cerebral cortex.

There are between 14 billion and 16 billion nerve cells in each of the six layers that make up the cerebral cortex. The brain's gray matter, which is located in the outer layer, is made up of nerve cell bodies, including dendrites, the end of nerves.

Therefore, Option A is correct.

Learn more about cortex from here:

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Answer:

(a). 300r + 425p ≤ 6,600

(b). No, it’s not considered overweight

Step-by-step explanation:

In this question, we are to write an equation that shows the number of refrigerators and pianos the truck could carry.

Let the number of refrigerators be r and the number of pianos be p

By using their individual weights, the equation is as follows;

300r + 425p ≤ 6,600

To the second question, we want to consider if 10 refrigerators and 8 pianos are overload.

To get this, we simply multiply the number of each by their individual weights;

That would be;

300(10) + 425(8) = 3000 + 3,400 = 6,400 lbs

This is not considered overweight as it is less than 6,600 lbs

Answer:

$11.57

Step-by-step explanation:

Let's call the price of the coffee two years ago by X.

The price increased 10% per year (that is, the price is multiplied by 1+0.1=1.1) over two years, so the current price is:

X * 1.10 * 1.10 = X * 1.21

If the current price is $14, we have that:

X * 1.21 = 14

X = 14/1.21 =  11.57

The price of the coffee two years ago was $11.57

Answer:

The 99% confidence interval is (553.7523, 582.2477)

Step-by-step explanation:

The formula for the confidence interval is

[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]

Where:

s = Standard deviation

z = t[tex]_{df}[/tex] since the population variance is unknown

df = Degrees of freedom

n = Sample count

Which gives

[tex]568 \pm t_{79}(0.05\%) \frac{48.28}{\sqrt{80} }[/tex]

= 568 [tex]\pm[/tex] 2.64×5.4

(553.7523, 582.2477)

That is there is a 99% chance that the mean weight of a jar of jelly is

553.75 < μ < 582.25.

Answer:

Step-by-step explanation:

Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.

We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]

That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.

Now the area of a semicircle is

[tex]A=\frac{\pi r^2}{2}[/tex] cubic units

Let r = y  and [tex]y^2=9-x^2[/tex]

Then area of the semicircle crossing the x-axis at x is  given by

[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units

[tex]=\frac{1}{2}\pi(9-x^2)[/tex]    

 Now we can find the definite integral of A(x) from x = -3 to x = 3.

Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.

We have that

[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]

[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]

[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]

[tex]=\pi[27-\frac{27}{3}][/tex]

[tex]=\pi[27-9][/tex]

[tex]=\pi[18][/tex]

[tex]=18\pi[/tex]

The volume of the solid is 18π cubic units.

The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.

To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².

The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).

The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:

V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx

This simplifies to:

V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx

We solve the integral:

V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)

Evaluating this, we get:

V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]

V = (π/2) [(27 - 9) - (-27 + 9)]

V = (π/2) [18 + 18]

V = (π/2) 36

V = 18π

Thus, the volume of the solid is 18π cubic units.

Answer:

The final value owed will be $3416.29.

Step-by-step explanation:

Since this is a compound interest problem we should use the apropriate formula given bellow:

M = C*(1 + r/n)^(n*t)

Where M is the final amount, C is the initial amount, r is the interest rate, t is the total time and n is the rate at which it is compounded. Since it's semiannually the value of n is 2 and we can use the formula to find the desired value.

M = 2000*(1 + 0.11/2)^(2*5)

M = 2000*(2/2 + 0.11/2)^(10)

M = 2000*(2.11/2)^(10)

M = 3416.29

The final value owed will be $3416.29.

Answer:

the distance travelled in 3 3/4 hours is 37/8 km

Answer: d.16 days

Step-by-step explanation:

Hi, using  PERT technique we can calculate the mean by applying the next formula:

Mean = (a + 4m + b)/6

Where:

a = optimistic time

m = most likely time

b = pessimistic time

Replacing with the values given:

Mean = (12 +4 (15) + 24)/6

Solving

m = (12+ 60+24)/6

m= 96/6

m = 16 days

Feel free to ask for more if needed or if you did not understand something.

Answer:It would be a decrease of 40 percent

Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%

Answer:

40 % decrease or -40%.

Step-by-step explanation:

The decrease is 10 - 6 = 4 feet.

% decrease = (4/10) * 100

= 0.4 * 100

= 40 % decrease.

Since the odds against choosing the lemon-flavored piece wasn't included, let us now assume that it is 2/5

Answer:

The Probability of choosing a lemon-flavored piece is 5/7

Step-by-step explanation:

Please kindly see the attached files for explanation

Complete question is;

In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?

Answer:

Total distance of race = 17.1875 miles

Step-by-step explanation:

The 3 parts of the race are; cycling, running and kayaking.

The cycling distance was; 12½ miles

We are told that the running part was ¼ of the cycling distance. Thus;

Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles

Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;

Kayaking distance = ½ x 25/8 = 25/16

Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles

Answer: n=4

Step-by-step explanation: 1:4 = 6:24

Answer:

X = 1.183

Step-by-step explanation:

X/6.5=0.1820

Multiply each side by 6.5

X/6.5 * 6.5=0.1820*6.5

X = 1.183

Answer:

Last one: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Answer:Answer:

Last One: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

Step-by-step explanation:

Answer:

( x - 9 )( x - 3 )

Step-by-step explanation:

plz give brainliest

Answer:

[tex]d = |h - 0\,ft|[/tex], The driver is 350 feet below sea level.

Step-by-step explanation:

The distance of the driver from the sea level is given by the following expression:

[tex]d = |h - 0\,ft|[/tex]

[tex]d = |-350\,ft-0\,ft|[/tex]

[tex]d = |-350\,ft|[/tex]

[tex]d = 350 \,ft[/tex]

The driver is 350 feet below sea level.

Answer:

Driver is 350 Below sea Level

Step-by-step explanation:

Driver has Elevation of -350 meters, negative indicates below sea level.

Therefore it can be inferred that the driver is 350 below sea level.

The answer is zero (0), when you add any number to it's opposite you always get zero

Answer:

the answer is 5

Step-by-step explanation:

YW

Answer:

There are 5 faces in a triangular prism

I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!