The speed of the current will be 8.89 miles per hour.
Given that,
The constant speed of motorboat = x = 48 miles per hour
And,
The Time taken by boat to make the upstream trip = 19/60 hour
And,
The Time taken by boat to make the return trip = 13/60 hour
Now,
According to the question,
Let,
The speed of the current = y miles per hour
And,
The total distance covered = z miles
And,
We know that,
Speed = Distance/Time
So,
For the upstream trip,
x - y = z/(19/60),
So,
z = (x-y) * (19/60) .....(i)
And,
For downstream trip
x + y = z/(13/60)
So,
z = (x + y) * (13/60) .....(ii)
From equations (i) and (ii),
We get,
(x - y) * (19/60) = (x + y) * (13/60)
i.e.
(48 - y) * (0.32) = (48 + y) * (0.22)
On solving we get,
15.36 - 0.32y = 10.56 + 0.22y
We get,
0.54y = 4.8
y = 4.8/0.54 = 8.89 miles per hour
So,
The speed of current = 8.89 miles per hour
Hence we can say that the speed of the current will be 8.89 miles per hour.
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3^2*7^8*13^6 /21^2*91^3
Answer:
1897612903782531117or9×
John and Sam have a lawn mowing service. At one home, John can mow the lawn by himself in 2 hours, but it takes Sam 2.5 hours. How many hours twill it take them to mow the same lawn
together? Give the answer correct to one decimal place.
Answer:
3/5 hours or 36 minutes
Step-by-step explanation:
John could mow three of these lawns in three hours (3/1 = three), while Sam could only mow two in three hours (3/1.5 = two). Therefore, the two of them could cut 5 lawns in 3 hours (3+2). Together, they can cut the same lawn in three and a half hours, or 36 minutes.
The 100th term of 1, 7, 13, 19, … is
[tex]Consider \: the \: sequence \: u_{n} \\ u_{n} \: appears \: to \: be \: arithmtic[/tex]
Quick Proof:[tex]u_{4}-u_{3}=u_{3}-u_{2}=... \\ 19 - 13 = 13 - 7 = .. \\ 6 = 6 = ...[/tex]
[tex]u_{n} \: is \: arithmetic \: with \: d = 6 \:and \: u_{1} = 1 \\ [/tex]
[tex]u_{n} = u_{1}+(n-1)d \\ u_{100} = 1 + (100 - 1)6 \\ u_{100} = 595[/tex]
The sum of 3 times a number and -8 added to 7 times the number
Answer:
(3x+-8) + 7x
Pls mark brainliest
A patient is to receive 0.25 mg of Medication A per kg of body weight per day. If the patient is a 157 lb man, how much medication A will he need?
The patient needs 17.66 mg of medication A .
Unitary method is "A way of finding a single-unit value from a multi-unit value, and then finding a multi-unit value from a single-unit value."For simplicity, always write what you calculate on the right and what you know on the left.In order to do that, we must first find the value of one thing by division and then find the value of more or fewer things by multiplication.It is given that a patient has weight 157 lbs.
We apply division because we need to find the cost of one item given the cost of many items. If you need to find the cost of many items from the cost of one item, apply the multiplication operation.
We need to convert this weight in kilogram using unitary method , we get 1 pound have = 0.45 kilogram
157 pound will have [tex]=157\times0.45[/tex]
[tex]=70.65[/tex] kilogram
A patient receive 0.25 mg of Medication A per kg
Using unitary method , we get
1 kg of body receives = 0.25 mg of medication A
70.65 kg of body receives [tex]=0.25\times 70.65[/tex]
[tex]=17.66[/tex] mg of medication A
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Compute the derivatives at the given value of a
1) The derivative of the function g(x) = (3x - 5)/(x - 2) at a = 1 is; g'(1) = -1
2) The derivative of the function f(x) = √(3x - 4) at a = 2 is; 3/(2√2)
What is the Derivative of the Function?1) We want to find the derivative of the function g(x).
g(x) = (3x - 5)/(x - 2)
g'(x) = -1/(x - 2)²
Thus;
g'(1) = -1/(1 - 2)²
g'(1) = -1
2) We want to find the derivative of the function f(x).
f(x) = √(3x - 4)
f'(x) = 3/(2√(3x - 4))
f'(2) = 3/(2√(3(2) - 4))
f'(2) = 3/(2√2)
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Please answer correctly, my grade depends on it also i'd help if you asnwer my other questions but only if you want to.
The domain are the independent variables for which an expression or equation exists. The domain of the graph in interval notation will be [-9,7]
Domain of a graph.The domain are the independent variables for which an expression or equation exists.
The given graph is described as a piecewise function since there are several lines that make up the graph.
The domain of the function are the value that lies along the x-axis of the line graph while the range are values of the function along the y-axis of the line graph.
The domain of the graph in interval notation will be [-9,7]. Note that both brackets are closed since the circles are shaded.
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Solve and put your final answer in the box
2 1/3 × -4/5
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3. Then the number is divisible by 3 Then the number is divisible by 9 If a number is divisible by 3 If a number is divisible by 9
Correct conclusion for statement : When a number is divisible by 9, the number is divisible by 3 is "the number is divisible by 3".
What is statement and conclusion ?
The statement and conclusion section is basically a logical reasoning section, in which a statement is given followed by a few conclusions from which you are supposed to choose the one that makes the most sense logically after the statement.
The statement provided is:
When a number is divisible by 9, the number is divisible by 3.
The general form of a conditional statement in if-then form is :
p → q
This implies that if p, then q.
The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.
The if-then form of the provided statement is:
If a number is divisible by 9, then the number is divisible by 3.
So, the conclusion is:
"the number is divisible by 3"
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Answer: A (then the number is divisible by 3)
Step-by-step explanation: did it on edge
OMG PLS HELP ME!!!! 30 pts!!!!! I NEED DIS ASAP
A large downtown hotel consists of twenty-four levels. Any level above ground is referred to as a" floor". There are twenty-two floors and each floor corresponds to its number on the number line (2 is second floor, 3 is third floor, etc...) and two underground levels reserved for underground parking. The first level below ground level is Parking A, and the second level below ground level is labeled Parking B.
If you start at Parking B and take the elevator to the fourteenth floor, how many levels have you gone up? [Type your answer as a number.]
Answer:
16
Step-by-step explanation:
there is 2 underground and 14 above so 2 + 14 = 16
Find the cost per pound of coffee mixture made from 8 pounds of coffee that cost $9.70 per pound in 14 pounds of coffee that cost $5.30 per pound?
Answer:
The total amount of the new coffee mixture would be:
8 + 12 = 20 (pounds)
The price of 20 pounds of coffee mixture would be:
8(9.2) + 12(5.5) = 139.6 (dollars).
Therefore, the average price would be:
139.6/20=6.98 (dollars).
Answer: $6.98 per pound.
A cargo truck is traveling 70 miles per hour and plans to travel 840 miles, plus or minus 105 miles, depending on fuel levels. Fnd the minimum and maximum number of hours the truck will travel at that speed.
The minimum is 10.5 hours and the maximum is not 12.2 hours.
The minimum and a maximum number of hours the truck will travel at that speed are 10.5 and 13.5 hours respectively.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Average velocity = total distance / total time taken
Units of velocity are given by ⇒ meter/second
Speed of truck = 70 miles/hour
Maximum distance = 840 + 105 = 945 miles.
Minimum distance = 840 - 105 = 735 miles.
Now,
Time = distance / velocity
Minimum time = minimum distance / velocity
So,
Minimum time = 735 / 70 = 10.5 hour.
Maximum time = maximum distance / velocity.
Maximum time = 945 / 70 = 13.5 hour.
Hence "The minimum and a maximum number of hours the truck will travel at that speed are 10.5 and 13.5 hours respectively".
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The function y = 2.5x + 3 can be used to determine the cost in dollars for a taxi ride of x miles.
What is the rate of change of the cost in dollars with respect to the number of miles?
$5.50/mile
$1/mile
$3/mile
$2.50/mile
Answer:
C. $2.50
Step-by-step explanation:
x=1 y=5.5
x=2 y=2.5
f / 5 -12 = -15. what does f equal to?
Answer:
f = -15
Step-by-step explanation:
f/5 - 12 = -15
+12 | +12
f/5 = -3
*5 | *5
f = -15
What number is composed of 6 hundreds, 30 ones, 2 tenths, 4 hundredths, and 6 thousandths?
6 hundreds+ 30 ones = 630
630 + 2 tenths+ 4 hundredths + 6 thousandths=
630.246Abigail buys eggs and oranges at the store.
• She pays a total of $14.71.
• She pays a total of $4.48 for the eggs.
• She buys 3 bags of oranges that each cost the same amount.
Write and solve an equation which can be used to determine x, how much each bag
of oranges costs.
that's, she pays $4.48 for eggs.. that simple means that orange is also the same amount of the egg,,,
$4.48×3=$13.44
i.e X=$13.44
in the following figure what is the value of y in terms of x?
a. x + 80
b. 80 - x
c. x + 100
d. x - 100
f. 100 - x
A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles? Answer quick hurry
Answer:
280 minutes
Step-by-step explanation:
The new distance travelled is 2.5 times larger than the previous (35/14 = 2.5), therefore, the new time needed to be travelled would also be 2.5 times larger than the original time taken.
[tex]112 \times 2.5 = 280[/tex]
Answer:
it will take her 280 minutes to travel 35 miles
Step-by-step explanation:
miles per hour = miles / hours
or in this case, miles / minutes
[tex]\frac{14 miles}{112 minutes}[/tex]
divide both the top and bottom by 112
[tex]\frac{0.125 miles}{1 minute}[/tex]
= 0.125 miles per minute
35 miles
[tex]35 / 0.125[/tex] = 280
280 minutes
translate the verbal phrases into an expressions
7 more than a number b b+
The algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.
What is an Algebraic Expression?A mathematical statement that is made up of operation signs (-, +), any variable (letters representing unknown quantity or number that varies), and numbers is referred to as an algebraic expression.
Algebraic expression are simplified or short form of translated phrases.
How to Translate Verbal Phrases into an Algebraic Expression?Let us represent the unknown number in the phrase as b.
"7 more than" means "+ 7".
Thus, the verbal phrase, "7 more than b" would be translated into an algebraic expression as:
b + 7.
Therefore, the algebraic expression for the verbal phrase, "7 more than a number b" is translated as: b + 7.
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Identify the type of function represented by f(x) = ½ • (5)ª.
OA. Increasing linear
OB. Decreasing linear
O C. Exponential growth
OD. Exponential decay
The correct answer is C. Exponential growth. As the function given f(x) = ½ • (5)ª is in exponential form, its range f(x) will increase for any input x.
What is termed as Exponential growth?Exponential growth happens when the larger you are, the faster you grow, making you even larger. Compound interest or population growth characterizes growth.It is termed exponential growth because it is only mathematically described by multiplying time by the exponent or power of the base. The population is then equal to some arbitrary number to a power of the growth rate multiplied by the time. Typically, the arbitrary number is 2, and the growth rate is given as the reciprocal of a doubling time.The given function is defined as;
f(x) = ½ • (5)ª
As, the function is written in the exponent form or power form , its is said to be exponential function.
Now, for any increasing value of x, the value of function will also increase but with increasing difference.
Thus, the function is termed as the exponential growth function.
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A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term of the sequence is 120, what is f(5)
Answer:
The sequence's fifth term is equal to 7.5.
Step-by-step explanation:
It is given in the question that A sequence is defined recursively using the formula f(n+1)=-0.5f(n) and we need to calculate f(5) if the first term of the sequence is 120.
Firstly,
The definition of a series is given by the formula f (n + 1) = -0.5 f. (n).
Now, what will be f(5) if the sequence's initial term is 120, let's calculate;
Recursively, a series is defined as follows;
=> f(n) = 120 if n = 1, otherwise.
Otherwise,
=> f(n) =-0.5f(n-1) if n > 1.
Now,
=> f(1) = 120
=> f(2) = -0.5f(1) = -0.5(120) = -60
=> f(3) = -0.5f(2) = -0.5(-60) = 30
=> f(4) = -0.5f(3) = -0.5(30) = -15
=> f(5) = -0.5f(4) = -0.5(-15) = 7.5
So, For n > 1, f(n) = (-0.5)(n-1) × 120
Therefore, the sequence's fifth term is equal to 7.5.
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1.7% of 35 is what number?
Answer:
0.595
Step-by-step explanation:
I multiplied 1.7 by 35 and moved the decimal.
Which of the following can be used to correctly solve the equation -1/3x=18?
____________________________________________________________________
1. Multiply both sides of the equation by -1/3
2. Divide both sides of the equation by -1/3
3. Multiply both sides of the equation by -3
4. Divide both sides of the equation by -3
5. Add 1/3 to both sides of the equation
6. Subtract 1/3 from both sides of the equation
Answer:The answer is the first one multiply both sides of the equation by -1/3
Step-by-step explanation:please give brainliest.
Crystal has 25 lollipops. Angie has 12 more lollipops than Crystal.
How many lollipops do the girls have all together?
Answer:
Both the girls have 62 lollipops
Step-by-step explanation:
25+25=50
50+12=62
Answer:
62 lollipops
Step-by-step explanation:
If Angie has 12 more lollipops than Crystal...
25 + 12 = 37 lollipops
Angie has 37 lollipops and Crystal has 25 lollipops. In total, that is...
37 + 25 = 62 lollipops
write ____ as a single power of 7
Answer:
[tex]7^{7/2}[/tex]
Step-by-step explanation:
[tex]7^3 \times \sqrt{7} \\ \\ =7^3 \times 7^{1/2} \\ \\ =7^{7/2}[/tex]
(8m-3n)(5m+9n) simplify
Answer:
40m² + 57mn - 27n²
Step-by-step explanation:
(8m - 3n)(5m + 9n)
each term in the second factor is multiplied by each term in the first factor, that is
8m(5m + 9n) - 3n(5m + 9n) ← distribute both parenthesis
= 40m² + 72mn - 15mn - 27n² ← collect like terms
= 40m² + 57mn - 27n²
Find the value of the power.
89⁰
Answer: 1
Step-by-step explanation:
Anything to the power of zero is one
Answer:
0.999847695
Step-by-step explanation:
1 for short ig :^
who travels the fastest explain why If two people answer and I see who is correct I will mark them brainlest
Answer: The jellyfish is faster
5,6 and 10 have a common multiple of 30 so make the denominator 30.
JF ->3/5=18/30
1/6=5/30
WR->5/6=25/30
3/10=9/30
9h-> 25 miles
1h->2.8 miles
5h->18 miles
1h->3.6 miles
Find x in the diagram below
Answer:
x=30 degrees
Step-by-step explanation:
both triangles are congruent therefor x will be the same as angle BAD
ill give brainly and 10 points
Answer: 135
Step-by-step explanation:
313 - 178 = 135