By setting the upstream and downstream distances equal and solving for the time rowed upstream, we find that the fisherman rowed 4.2 hours upstream and 2.8 hours downstream. Since he rowed back to his starting point, the total distance rowed upstream and downstream is the same, amounting to 33.6 miles for the entire trip.
To solve this problem, we need to determine how much time the fisherman spent rowing upstream and downstream. Let's call the upstream speed U, which is 4 mph, and the downstream speed D, which is 6 mph. He rows for a total of 7 hours. Let's call the time spent rowing upstream T and the time spent rowing downstream (7 - T) since the entire trip takes 7 hours.
Since distance equals rate times time, the upstream distance will be U × T and the downstream distance will be D × (7 - T). Because the fisherman returns to his starting point, the upstream and downstream distances are equal.
Setting them equal gives us the equation:
4T = 6 (7 - T)
Solving for T gives us:
T = 42 / 10 = 4.2 hours
Hence, the time spent rowing downstream is 7 - 4.2 = 2.8 hours.
To find the total distance rowed, we use the downstream distance (since it's equal to the upstream distance) which is calculated as:
Distance = D × (7 - T) = 6 × 2.8 = 16.8 miles
Therefore, the fisherman rowed a total of 16.8 miles upstream and 16.8 miles downstream, summing up to 33.6 miles for the entire trip.
4x^2+4y^2=64
what are the domain and range
What is the value of r? 35(r−7)=1
The answer is 8 and 2 over 3.
Which information from this passage about enkai is most important to include in a summary of the overall story?the tribe’s relationship with enkai is crucial to them.the tribe’s behavior affects enkai’s mood.enkai has moods that are reflected in the weather.enkai can be the black god or the red god
WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).
Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?
What is .62 rounded to the nearest tenth?
At the bank brent exchanges $50 in bills for 50 one-dollars coins. the total mass of the coins is 405 grams. estimate the mass of 1 one - dollar coin.
A pumpkin with a mass of 2.5 kg was pushed toward a wall. The average acceleration of the pumpkin was 10.7 m/s². How much force was applied to the pumpkin to make it move?
Simplify -3p3 + 5p + (-2p2) + (-4) - 12p + 5 - (-8p3). Select the answer in descending powers of p.
1 - 7p - 2p2 + 5p3
5p3 - 2p2 - 7p + 1
1 + 7p + 2p2 - 5p3
-5p3 + 2p2 + 7p + 1
Answer:
B. 5p³ - 2p² - 7p + 1
Step-by-step explanation:
Good luck! Hope it was found helpful to you!
A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?
The approximate probability of choosing one club followed by one heart from a standard deck of 52 playing cards is 5.9%.
The student's question pertains to the calculation of the probability of choosing one club and one heart from a standard deck of 52 playing cards. We start by recognizing that there are 13 clubs and 13 hearts in the deck, with each of the four suits represented equally.
Firstly, the probability of choosing a club (P(club)) is 13/52. After a club is chosen, there are 51 cards left in the deck. The number of hearts remains the same at 13 (since a club was chosen first). So, the probability of then picking a heart (P(heart)) is 13/51.
The two events, choosing a club and then a heart, are dependent events because the outcome of the second event depends on the outcome of the first. Hence, to find the combined probability, we multiply the probabilities of each event.
The probability of choosing one club followed by one heart is therefore P(club) imes P(heart) = (13/52) imes (13/51), which simplifies to approximately 0.059, or 5.9%.
what is another name for plane Z?
what is the answer to n * $3.25 = 325.00 ?
Perform the operations, multiply, and simplify.-a^3b (3a^2 b^5 - ab^4 - 7a ^2
b.
There are around 132 births in the united states per minute. how many births per day
Sarah is driving her car very smoothly from
Austin to Dallas one day. At 6:00 pm she is
travelling at 20 mph, while 25 minutes later
she is travelling at 40 mph.
Calculus tells us that at some time between
6:00 pm and and 6:25 pm her acceleration is
exactly x mph/h. Determine x.
The acceleration (x) is approximately 48 mph/hr, determined by dividing the change in velocity (20 mph) by the change in time (0.41667 hr).
Explanation:The subject of this problem is acceleration, which in this context refers to the rate at which Sarah increased her speed during a particular period of time. Here, the change in speed was from 20 mph to 40 mph, a difference of 20 mph. The time over which this change occurred was 25 minutes, but since acceleration is usually measured in hours, we need to convert this to 25/60 = 0.4167 hours.
The formula for acceleration is change in speed/ change in time.
Therefore, to calculate the acceleration, we divide the change in speed (20 mph) by the time (0.4167 hr) to get x = 20 mph / 0.4167 hr = 47.99 mph/hr or approximately 48 mph/hr, which is the acceleration.
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Which answer describes the type of sequence?
1, 6, 7, 13, ...
A. geometric
B. neither arithmetic nor geometric
C. arithmetic
b: neither arithmetic nor geometric
The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is a particular order.
The sequence is given in the question following as:
1, 6, 7, 13, ...
We have to identify the type of given sequence
As per the given question, we have
1, 6, 7, 13, ...
For checking as an arithmetic sequence :
Common difference between 1 and 6 is d = 6 - 1 = 5
Common difference between 6 and 7 is d = 7 - 6 = 1
Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.
For checking as a geometric sequence :
Common ratio between 1 and 6 is r = 6/1 = 6
Common ratio between 6 and 7 is r = 7/6
Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence
Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.
Learn more about arithmetic sequence here:
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Solve 16 1/2 ÷ 2 1/4
A:7 1/3
B:5 3/7
C:133/8
How many different 12-member juries can be made from 150 people? Please explain how. Thank you (:
Crafty Grandma Edith sat her family down during Thanksgiving and told them they couldn’t have any pumpkin pie until they worked out this puzzle. Her 6-year-old granddaughter was the first to solve it! Can you work out what 9183 equals?
8809=6
7111=0
9881=5
6660=4
5531=0
2516=1
3590=2
6855=3
1012=1
5731=0
9191=2
9183=?
a 14 foot ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building does the ladder reach?
Using the sine function and known angle and ladder length, the distance up the building the ladder reaches is \(7\sqrt{2}\) feet.
The correct answer is option C) \(7\sqrt{2}\) feet.
To find how far up the building the ladder reaches, we can use trigonometric functions, specifically the sine function since we have the angle and the length of the ladder.
Given:
- Length of the ladder (hypotenuse) = 14 feet
- Angle with the building = 45 degrees
Let [tex]\(x\)[/tex]be the distance up the building that the ladder reaches.
Using the sine function [tex](\(\sin\))[/tex] in a right triangle:
[tex]\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \][/tex]
Substituting the known values:
[tex]\[ \sin(45^\circ) = \frac{x}{14} \][/tex]
Since [tex]\(\sin(45^\circ) = \frac{\sqrt{2}}{2}\),[/tex] we have:
[tex]\[ \frac{\sqrt{2}}{2} = \frac{x}{14} \][/tex]
To solve for [tex]\(x\),[/tex] multiply both sides by 14:
[tex]\[ x = 14 \times \frac{\sqrt{2}}{2} \][/tex]
[tex]\[ x = 7\sqrt{2} \, \text{feet} \][/tex]
Therefore, the ladder reaches [tex]\(7\sqrt{2}\)[/tex] feet up the building.
Therefore the correct answer is option C) [tex]\(7\sqrt{2}\)[/tex]feet.
The question probable may be:
A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach?
A. 7 feet
B. 28sqrt(2) feet
c. 7sqrt(2) feet
D. 14sqrt(2) feet.
At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?
a. x + y < 12
b. x + y > 12
c. x + y ≤ 12
d. x + y ≥ 12
the answer is B hope it helps
Which of the following is a factor of 2x4 + 22x3 + 60x2?
2x3
x4
x + 4
x + 5
the correct answer is x+5 :DDD it was also the correct answer on the test !
Final answer:
To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. The only option that is a factor of the given expression is x⁴.
Explanation:
To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. Let's test each option:
2x³: When we divide 2x⁴ + 22x³ + 60x² by 2x3, the remainder is not zero. Therefore, 2x3 is not a factor.
x⁴: When we divide 2x⁴ + 22x³ + 60x²by x4, the remainder is zero. Therefore, x4 is a factor.
x + 4: When we divide 2x⁴ + 22x³ + 60x² by x + 4, the remainder is not zero. Therefore, x + 4 is not a factor.
x + 5: When we divide 2x⁴ + 22x³ + 60x² by x + 5, the remainder is not zero. Therefore, x + 5 is not a factor.
Based on the results, the only option that is a factor of the given expression is x⁴.
determine the differential equation giving the slope of the tangent line at point (x,y) for the given family of curves.
x^2+y^2=2cx ...?
Solve: log2 (x) +log2(x+7) =3
(2 is the base) ...?
Final answer:
To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.
Explanation:
To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.
A circle has an area of 98mm^2. Find the circumference of the circle
Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61,600, how much does Tina pay in state income tax?
a. $1,545
b. $227
c. $4,372
d. $2,772
Transform the formula for the given variable: I=Prt solve for t
A movie store sells DVDs for $11 each. What is the cost of n DVDs? Identify the situation as discrete or continuous.
A) C= 11n; continuous
B) C= 11+n; discrete
C) C= 11+n; continuous
D) 11n; discrete
Answer:
Complete Quick Check of...
Lesson 4: Graphing a Function Rule
Algebra 1 A: Unit 5
Step-by-step explanation:
1.C) x,0,1,2,3, y,3,-1,-5,-9
2.A) True
3.D) $698.75
4.C) cant write it out.
5.D) C = 11n; discrete
:) hope this helps!
In ELECTRONICS, the total resistance to the flow of electricity in a circuit is called the impedance, Z. Impedance is represented by a complex number. The total impedance in a series circuit is the sum of individual imepedances. The impedance in one part of a circuit is Z1 = 3 + 4i. In another part of a circuit, the impedance is Z1 = 5 - 2i. What is the total impedance of the circuit?
The total impedance of the circuit is 8 + 2i.
Explanation:The total impedance in a series circuit is the sum of the individual impedances. To find the total impedance of the circuit, add the real parts and imaginary parts separately. In this case, Z1 = 3 + 4i and Z2 = 5 - 2i. So, the total impedance Zt = (3 + 5) + (4 - 2)i. Simplifying this, Zt = 8 + 2i.