Find the solution to the system
of equations.




please help

The speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.

Given to us

Speed of the boat = 5 mph

It takes the boat 3 hours to travel upstream

2 hours to travel the same distance downstream

Let the distance traveled by boat be L.

We know that when the boat is going upstream the water current will provide resistance to the boat, therefore,

\(L = (S_c-S_b)\times T_u\)

where L is the distance traveled by boat, \(\rm S_c\ and\ S_b\) are the speed of current and boat respectively, And \(T_u\) is the time of the boat during the downstream journey.

\(L = (S_c-5)\times 3\)

We know that when the boat is going downstream the water current will provide help to the boat, therefore,

\(L = (S_c+S_b)\times T_d\)

\(L = (S_c+5)\times 2\)

We already have two-equation for the distance traveled by boat therefore, we will equate both the equations,

\((S_c-5)\times 3 = (S_c+5)\times 2\)

\(3S_c-15= 2S_c+10\\\\3S_c-2S_c = 10+15\\\\S_c = 25\rm\ mph\)

Hence, the speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.

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Answer:

5mph

Step-by-step explanation:

edge2022

The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².

The area of triangle can be determined using the equation;

Area = 1/2 × base × height.

The angle described forms a right-triangle.

Area = 1/2 × base × height

Area = 1/2 × 12cm × 15cm

Area = 6cm × 15cm

Area = 90 cm²

Therefore, the area of the triangle is 90 cm².

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Sam's experimental probability of getting heads in 30 coin flips was 20 out of 30, while the theoretical probability of getting heads is 1/2 or 0.5.

Sam's experimental probability of getting heads in the 30 coin flips was 20 out of 30, which can be written as 20/30 or simplified to 2/3. This means that in the experiment, heads appeared in approximately two-thirds of the flips. On the other hand, the theoretical probability of getting heads in a fair coin flip is 1/2 or 0.5. This is because there are two equally likely outcomes (heads or tails) and only one of them is heads.

Comparing the experimental and theoretical probabilities, we can see that Sam's results deviate slightly from the expected outcome. The experimental probability of getting heads is higher than the theoretical probability. This could be due to chance or random variation, as 30 coin flips may not be enough to perfectly represent the true probability. With a larger number of trials, the experimental probability would tend to converge towards the theoretical probability. However, in this specific experiment, Sam's results suggest a slightly biased coin favoring heads.

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The situation involving the food establishment has a probability of "2.08 % " points higher than the situation involving the financial establishment

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The question is incomplete, as the required table which is not given.

we have the following parameters:

The probability that the establishment earns up to $25k = 10.59%

The probability that the establishment earns between $25k - $50k or $50k - $75k = 8.56%

Using the above values, the difference in the probabilities are;

d = 10.59% - 8.56

d = 2.03%

Hence, the true statement about the probability is option (d)

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The probability that at most 2 out of 6 randomly sampled people from the city are unemployed is 0.8474, rounded to two decimal places.

To find the probability that at most 2 out of 6 randomly sampled people from the city are unemployed, we can use the binomial probability formula.

The formula for the probability of getting exactly x successes in n independent Bernoulli trials, each with a probability of success p, is:

\(P(X = x) = (nCx) * (p^x) * ((1-p)^{(n-x)})\)

In this case, the number of trials n is 6, the probability of success (unemployment) p is 0.12 (12% as a decimal), and we want to find the probability for at most 2 unemployed people, so we sum up the probabilities for x = 0, 1, and 2.

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Let's calculate each probability:

\(P(X = 0) = (6C0) * (0.12^0) * (0.88^6) = 1 * 1 * 0.4177 = 0.4177\)

\(P(X = 1) = (6C1) * (0.12^1) * (0.88^5) = 6 * 0.12 * 0.4437 = 0.3197P(X = 2) = (6C2) * (0.12^2) * (0.88^4) = 15 * 0.0144 * 0.5153 = 0.1100\)

Now, let's calculate the cumulative probability:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4177 + 0.3197 + 0.1100 = 0.8474

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Answer:

33

Step-by-step explanation:

Answer:

the answer is 632

Step-by-step explanation:

just do some normal multiplication. :)  

The rate of change for the functions represented by graph 1 and graph 2 is the same.

What is slope?

Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line.

To compare the rates of the two functions represented in the graphs, we need to find the slopes of the lines.

For graph 1, the slope can be calculated as follows:

slope = (change in y) / (change in x)

Let's choose the points (2, 3) and (8, 0):

change in y = 0 - 3 = -3

change in x = 8 - 2 = 6

slope = -3/6 = -1/2

Now let's choose the points (-2, 5) and (-6, 7):

change in y = 7 - 5 = 2

change in x = -6 - (-2) = -4

slope = 2/(-4) = -1/2

So the slope of the line for graph 1 is -1/2.

For graph 2, the slope can be calculated as follows:

slope = (change in y) / (change in x)

Let's choose the points (0, 1) and (5, 0):

change in y = 0 - 1 = -1

change in x = 5 - 0 = 5

slope = -1/5

Now let's choose the points (-5, 2) and (0, 1):

change in y = 1 - 2 = -1

change in x = 0 - (-5) = 5

slope = -1/5

So the slope of the line for graph 2 is also -1/5.

Comparing the slopes, we can see that the slopes of the lines for graph 1 and graph 2 are the same.

Therefore, the rate of change for the functions represented by graph 1 and graph 2 is the same.

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The required quotient would be 66 8/25 or 66.32 which is determined by dividing 1,658 by any divisor 25.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have to determine the quotient.

⇒ 1,658 ÷ 25

Apply the Division operation, and we get

⇒ 1,658 / 25

⇒ 66.32

⇒ 66 8/25

Therefore, the required quotient would be 66 8/25 or 66.32.

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Answer:

Wind causes blade to move

Step-by-step explanation:

As blade moves, turbine work, and thus v get electricity from wind

Have a GOOD DAY.....

Answer:

8.6

Step-by-step explanation:

A^2+B^2=C^2

5^2+7^2=C^2

25+49=C^2

74=C^2

√74=C

C=8.6

The length QR of the right angle triangle is 26 cm.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of a right angle triangle can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

24² + 10² = QR²

576 + 100 = QR²

QR² = 676

QR = √676

QR = 26 cm

Therefore,

length of QR = 26 cm

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The geometric solid suggested by a typical American house is:

d. Prism

A typical American house often has a rectangular base and parallel, congruent faces.

This shape is best represented by a rectangular prism.

The geometric solid suggested by a typical American house is a prism, specifically a rectangular prism.

A prism is a three-dimensional solid that has two congruent and parallel bases that are connected by a set of parallelograms.

A rectangular prism has two rectangular bases and rectangular faces that are perpendicular to the bases.

Most American houses are rectangular in shape and have a flat roof, which suggests that they are in the form of a rectangular prism.

The walls of the house form the rectangular faces of the prism, and the roof forms the top face of the prism.

The rectangular shape of the house provides a practical and functional design that allows for efficient use of interior space.

It is also an aesthetically pleasing design that has become a standard for American homes.

d. Prism.

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The equation to determine the velocities of boxes is given by, v² = 2*a*d

To determine the velocities of the boxes when they move a distance d down the slope after being released from rest, we can use the following terms: velocity, box, and distance (d). Here's a step-by-step explanation:

1. Since the boxes are released from rest, their initial velocity (v0) is 0.
2. Let's assume the slope has an angle (θ) and the acceleration due to gravity (g) is 9.81 m/s².
3. Calculate the acceleration (a) of the boxes down the slope using the formula: a = g * sin(θ).
4. To find the final velocity (v) of the boxes after traveling a distance (d) down the slope, we can use the equation: v² = v0² + 2*a*d.

Since the boxes are released from rest, v0 is 0. Therefore, the equation simplifies to:

v² = 2*a*d

Now, substitute the acceleration (a) and distance (d) into the equation and solve for the final velocity (v) of the boxes.

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Answer:

LM = 38.4

Step-by-step explanation:

8/LM = 5/24

5LM = 192

LM = 38.4

Answer:

i need the answer

Step-by-step explanation:

Answer:

It's probably an isosceles triangle

Step-by-step explanation:

Answer:

If it's AL to A'L' then its 1/2

If it's A'L' to AL then its 2

Answer:

(5, 6)

Step-by-step explanation:

When I see "use technology," I'm assuming that your teacher is allowing you to use some kind of graphing calculator to find the solution, so that's what I'm going to do.

On Desmos, which is an online graphing calculator, I entered both equations and two lines showed up on the graph. The point of intersection, or solution, is emphasized on the graph: (5, 6). I encourage you to try this for yourself, since it's pretty easy, but I've attached a screenshot of the graph that I was able to make just in case you're still confused.

Hopefully that's helpful! :)

The greatest possible number is 5 minutes.

To find the greatest possible number of minutes each girl spent on each valentine, we need to determine the common divisor of the time spent by Mariam, Sandy, and Christi.

The time spent by Mariam is 25 minutes, the time spent by Sandy is 20 minutes, and the time spent by Christi is 30 minutes.

To find the greatest common divisor (GCD) of these numbers, we can list their factors and find the largest common factor:

Factors of 25: 1, 5, 25

Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

The largest common factor among these numbers is 5.

Therefore, the greatest possible number of minutes each girl spent on each valentine is 5 minutes.

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What problem. You didn't attach anything or put it in the question.

The measure of angle PSR in a kite PQRS, is equals to the 60°.

We have a kite PQRS, present in above figure. The measure of angle QPO = 50°

The measure of angle QRO = 70°

We have to determine the measure of angle PSR. As we see in figure, there is four right angled triangles as ∆POQ, ∆OQR , ∆POS and ∆OSR.

measure of angle POS = measure of angle SOR = 90°

measure of angle SPO = measure of angle QRO = 70° ( Since alternative angles)

Similarly, measure of angle SRO

= measure of angle QPO = 50° ( Alternative angles )

So, measure of angle PSR = measure of angle PSO + measure of angle RSO --(1)

Measure of angle RSO = 180° - measure of angle ROS - measure of angle SRO

= 180° - 90° - 50° = 40°

Also, Measure of angle PSO = 180° - measure of angle POS - measure of angle SPO = 180° - 90° - 70° = 20°

So, from equation (1),

measure of angle PSR = measure of angle PSO + measure of angle RSO

= 40° + 20°

= 60°

Hence, required measure of angle is 60°.

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Complete question:

The above figure completes the question. In kite PQRS, measure of angle QPO=50° and measure of angle QRO=70°. Find measure of angle PSR.

Answer:

\( \sqrt{30} \)

Answer:

64.8°

Step-by-step explanation:

A

Please see attached a rough sketch for your reference

Step one:

Given data

the distance you are standing from the building represent the adjacent =400ft

and the height of the building represents the opposite= 850ft

Step two:

Required is the angle of elevation

applying SOH CAH TOA

Tan ∅= opp/adj

Tan ∅= 850/400

Tan ∅=2.125

∅=Tan-1(2.125)

∅=64.8°

The angle of elevation 64.8°

You can use the fact that buildings are usually standing perpendicular to the ground and ground for smaller distance acts as if its a straight plane.

The measurement of angle of elevation is \(64.798^\circ\)

What you see something higher than your eye level height, you need to see up, you elevate your head to see that thing. The angle from the straight horizontal level of eye to the current elevated level is measured and named as angle of elevation.

Similarly, there is angle of depression when the observer looks down.

See the figure attached below to understand the symbols used in calculations.

Since the building is 850 ft tall, we can assume that our height is almost 0 in comparison to this building (the angle deduced then will be approximately equal to the real angle).

Let you're standing on point O

Let the building's base is point A.

Let the top of the building is tagged as point E.

Then we have:

Length of OA = 400 ft.

Length of AE = 850 ft.

To find: angle AOE.

\(tan(\angle AOE) = \dfrac{AE}{OA} = \dfrac{850}{400} = 2.125\\\\ m\angle AOE = arctan(2.125) = 64.798^\circ \text{\: (from calculator)}\)

Thus, the measurement of angle of elevation is \(64.798^\circ\)

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The distance from the point (1,2) to the line 4x - 3y = 0 is 2/5 units.

To find the distance between a point and a line, we need to use the formula:

distance = |ax + by + c| / √(a^2 + b^2)

where a, b, and c are the coefficients of the equation of the line in the form ax + by + c = 0. In this case, the equation of the line is 4x - 3y = 0, so a = 4, b = -3, and c = 0.

To apply the formula, we need to find the values of x and y that correspond to the point (1,2) when they are plugged into the equation of the line. Solving for y in terms of x, we get:

4x - 3y = 0

-3y = -4x

y = (4/3)x

Now we can plug in the coordinates of the point (1,2) and find the distance:

distance = |4(1) - 3(2) + 0| / √(4^2 + (-3)^2)

= |-2| / √(16 + 9)

= 2 / √25

= 2/5

Therefore, the distance from the point (1,2) to the line 4x - 3y = 0 is 2/5 units.

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There is a 50% chance that both students are upperclassmen.

Given: Two students meet at a library, where at least one of them is an upperclassman who is currently taking EECS 126, assume each student is an upperclassman and underclassmen with equal probability and each student takes 126 with probability 1/10, independent of each other and independent of their class standing. To find: Probability that both students are upperclassmen.

Solution: Let P(A) be the probability that a student is an upperclassman, and P(B) be the probability that a student is taking EECS 126.P(A) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability) P(B) = 1/10 (Given, each student takes 126 with probability 1/10, independent of each other and independent of their class standing) Let C be the event that both students are upperclassmen. Then, P(C) = Probability that both students are upperclassmen P(C') = Probability that one student is an underclassman or both are underclassmen P(C') = P(Ac) ...(i) P(C') = 1 - P(C) ...(ii) P(Ac) = P(underclassman) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability)

Now, P(C') = P(Ac) = 1/2 ...from (i) P(C) = 1 - P(C') = 1 - 1/2 = 1/2 Also, P(B) and P(A) are independent events as given in the question, So, P(AB) = P(A)P(B) = (1/2) x (1/10) = 1/20 Hence, the probability that both students are upperclassmen is P(AB) = 1/20.In other words, there is a 50% chance that both students are upperclassmen.

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Answer:

(1, 2)

(2,2)

Step-by-step explanation:

The inequality Given :

y < 5x + 2

y ≥ One-halfx + 1

We can use the values in the options to see which satisfies the inequality :

(-1, 3) ; X = - 1, y = 3

3 < 5(-1) + 2 ; 3 < - 4 (not true)

(0, 2) ; X = 0 ; y = 2

2 < 5(0) + 2 ; 2 < 2 (nor true)

2 > 1/2(0) + 1

2 > 1 (true)

Using (1, 2).; x = 1 ; y = 2

2 < 5(1) + 2 ; 2 < 7 (true)

2 > 1/2(1) + 1 ; 2 > 1.5 (true)

Using (2, 2)

y < 5x + 2

2 < 10 + 2 ; 2 < 12 (true)

y > 1/2x + 1

2 > 1/2(2) + 1 ; 2