Answer:
the rate / speed of the boat is 10 miles per hour.
the rate / speed of the current is 2 miles per hour.
Step-by-step explanation:
r = rate of boat (speed of boat)
t = time
d = distance.
c = rate of current (speed of current)
with the current, the formula becomes (r + c) * t = d
against the current, the formula becomes (r - c) * t = d
going with the current, the boat takes 1 hour to travel 12 miles.
therefore:
(r + c) * t = d becomes (r + c) * 1 = 12
going against the current, the boat takes 1.5 hour to travel the same 12 miles.
therefore:
(r - c) * t = d becomes (r - c) * 1.5 = 12.
your two equations that need to be solved simultancously are:
(r + c) * 1 = 12
(r - c) * 1.5 = 12
divide both sides of the second equation by 1.5 and leave the first equaion as is to get:
r + c = 12
r - c = 8
add the equations together to get:
2 * r = 20
solve for r to get:
r = 20 / 2 = 10
(r + c) * 1 = 12 becomes (10 + c) * 1 = 12
simplify to get 10 + c = 12
solve for c to get c = 12 - 10 = 2
(r - c) * 1 = 8 becomes (10 - c) * 1 = 8
simplify to get 10 - c = 8
solve for c to get c = 10 - 8 = 2
you have:
r = 10
c = 2
that's your solution.
the rate / speed of the boat is 10 miles per hour.
the rate / speed of the current is 2 miles per hour.
ILL GIVE BRAINLIEST AND 50 POINTS PLS help
A cell phone company charges $50 connection fee plus $20 per line. Jake must spend under $140 on his family’s cell phone bill. How many cell phone lines can his family have? Write the linear inequaulity that models this situation then solve the problem
Answer: 2
bc 50+20=70
140 divided by 70 is 2
Step-by-step explanation:
Elena rode her bike 2 miles in 10 minutes. She rode at a constant speed. Complete the table to show the time it took her to travel different distances at this speed. Write your answer as a decimal.
Answer:
0.2
Step-by-step explanation:
2/10 or 1/5
Answer:
0.2
Step-by-step explanation:
The side of the base of a square pyramid is increasing at a rate of 666 meters per minute and the height of the pyramid is decreasing at a rate of 111 meter per minute. At a certain instant, the base side is 333 meters and the height is 999 meters. What is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)
Answer:
[tex]105m^3/min[/tex]
Step-by-step explanation:
We are given that
Base side of square pyramid, a=3 m
Height of square pyramid, h=9m
[tex]\frac{da}{dt}=6m/min[/tex]
[tex]\frac{dh}{dt}=-1/min[/tex]
We have to find the rate of change of the volume of the pyramid at that instant.
Volume of square pyramid, V=[tex]\frac{1}{3}a^2h[/tex]
Differentiate w.r.t t
[tex]\frac{dV}{dt}=\frac{1}{3}(2ah\frac{da}{dt}+a^2\frac{dh}{dt})[/tex]
Substitute the values
[tex]\frac{dV}{dt}=\frac{1}{3}(2(3)(9)(6)+(3^2)(-1)[/tex]
[tex]\frac{dV}{dt}=105m^3/min[/tex]
Hence, the rate of change of the volume of the pyramid at that instant=[tex]105m^3/min[/tex]
A. f(x) = 2|2| is differentiable overf
X
B. g(x) = 2 + || is differentiable over
-f
Recall the definition of absolute value:
• If x ≥ 0, then |x| = x
• If x < 0, then |x| = -x
(a) Splitting up f(x) = x |x| into similar cases, you have
• f(x) = x ² if x ≥ 0
• f(x) = -x ² if x < 0
Differentiating f, you get
• f '(x) = 2x if x > 0 (note the strict inequality now)
• f '(x) = -2x if x < 0
To get the derivative at x = 0, notice that f '(x) approaches 0 from either side, so f '(x) = 0 if x = 0.
The derivative exists on its entire domain, so f(x) is differentiable everywhere, i.e. over the interval (-∞, ∞).
(b) Similarly splitting up g(x) = x + |x| gives
• g(x) = 2x if x ≥ 0
• g(x) = 0 if x < 0
Differentiating gives
• g'(x) = 2 if x > 0
• g'(x) = 0 if x < 0
but this time the limits of g'(x) as x approaches 0 from either side do not match (the limit from the left is 0 while the limit from the right is 2), so g(x) is differentiable everywhere except x = 0, i.e. over the interval (-∞, 0) ∪ (0, ∞).
1+4=5
1+5=6
1+6=7
8+7=?
Answer:
8+7=15
Step-by-step explanation:
Just add 8+7 which will equal 15
Answer:
The answer is 15
Step-by-step explanation:
Hoped this helped!
Suppose that c is a number for which the equation c÷c = 1 is false. What is c?
Answer:
Hope it help
Mark me as brainliest
Step-by-step explanation:
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
A car is traveling along a test track in the desert at a constant rate of 85 feet per second The test track has a length of 10,000 feet, and the track is marked by foot for observation purposes. After 8 seconds, the car is at foot marker 1000 feet. At what foot marker was the car at time t= 0 seconds?
Answer:
foot marker 320 at t=0
Step-by-step explanation:
8 sec x 85 ft/s =680 ft
1,000ft - 680 ft = 320 ft
At t = 0 seconds the car was at a foot marker of 320 feet.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, A car is traveling along a test track in the desert at a constant rate of 85 feet per second.
After 8 seconds, the car is at foot marker 1000.
So, In those 8 seconds, the car has traveled (8×85) = 680 feet.
Therefore, Initially, the car was at (1000 - 680) feet.
= 320 feet.
learn more about numerical expressions here :
https://brainly.com/question/29199574
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I need some help!!!Please
Answer: I think it's Sporting Life:)
hope this help!
Answer:
66
Step-by-step explanation:
added and dont stop untill the end
Need help ASAP Question 1 of 10
If g(x) = 4x2 - 16 were shifted 9 units to the right and 1 down, what would the
new equation be?
Answer:
4(x - 9)^2 - 17
Step-by-step explanation:
A horizontal shift to the right by 9 changes x^2 to (x - 9)^2.
A vertical shift down by 1 changes - 16 to -17.
Therefore, the new equation is:
4(x - 9)^2 - 17
Andrew had 30 dollars to spend on 3 gifts. He spent 8
1
4
dollars on gift A and 5
4
5
dollars on gift B. How much money did he have left for gift C?
Andrew has 17 dollars left for gift c
perimeter ILL MARK BRAINLY
Answer:
The perimeter is 24 in2
Step-by-step explanation:
You have to add up all of the sides together
Answer:
the answer 24
Step-by-step explanation:
P= 10+6+8=24 in
because perimeter is just adding
Please Help asap!! I will give brainly to whoever answer correctly! I need to submit this answer by today!
Which statement best describes the expression 3y ÷ 8?
(answer choices-
A- 8 divided by 3 times y
B- 8 times y divided by 3
C- 3 divided by 8 times y
D- 3 times y divided by 8
Answer:
C or D
Step-by-step explanation:
Answer:
I think option D 3 times y divided by 8
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Answer: they would both have $240 in 3 months
Step-by-step explanation:
180 + 20 + 20 + 20 = 240
120 +40 + 40 + 40 =240
-
180+20=200+20=220+20=240
120+40=160+40=200+40=240
and there u go :)
Write an equation of the parabola with focus (0, 10) and vertex at the origin
Answer:
f(x) = (1/10)x²
Step-by-step explanation:
This is the answer that I think it is but I am not sure if it is right...
Hope this helps!
5. Usa el método de cocientes parciales para hallar 1,032 ÷ 43.
the answer for the question is 24
.
Out of 20 cookies, 4/ 5 are chocolate chip. How many cookies are chocolate chip?
Answer:
16 cookies. Try your best.
Answer: 16
Step-by-step explanation:
We can solve this by using the equation: 4/5 x 20 = y
(y is the answer)
Now we can solve it. You can just solve 4/5 x 20, or if you like using decimals you can change it to 0.8 x 20, becaues 4/5 is equivalent to 0.8.
0.8 x 20 = 16.
Therefore, out of the 20 cookies, 16 are chocolate chip.
I really need help please can you help I’ll give brainlest to first person (please hurry)
Answer: 1/3
Step-by-step explanation:
Half of the 14 brown eggs are cracked so there are 7 cracked eggs. There are 7+14=21 eggs in total so the probability of getting a cracked egg that is brown is 7/21=1/3
Work out the equation of the line which has a gradient of 1/2 and
passes through the point (4, -2).
9514 1404 393
Answer:
y = 1/2x - 4
Step-by-step explanation:
The point-slope form of the equation for a line is a useful starting place when slope and point are given.
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y -(-2) = 1/2(x -4) . . . . line with slope 1/2 through point (4, -2)
y = 1/2x - 4 . . . . . . . . eliminate parentheses, subtract 2
A group of students with normally distributed salaries earn an average of 6800 with a standard deviation of $2500. Find the cutoff for the salary that corresponds to the lower 25% of all salaries
Answer: $5115
Step-by-step explanation:
The following information can be gotten from the question:
Mean = 6800
Standard deviation = 2500
We will then find the Z score of the 25th percentile which will be -0.674.
Therefore, the cutoff for the salary that corresponds to the lower 25% of all salaries will be:
= 6800 - 0.674 × 2500
= 6800 - 1685
= 5115
The cutoff is $5115
The Empire State Building in New York City
443.2 meters tall. This is 119.2 meters taller
than the Eiffel Tower in Paris. Which equation
can be used to find the height h in meters of
the Eiffel Tower?
Hurry please, thanks!
The total number of points scored during 10 regional games is shown below.
52, 51, 65, 38, 56, 48, 50, 31, 46, 31
Select the correct five-number summary for this data set. (4 points)
Answer:
Min 31
Q1 38
Median 49
Q3 52
Max 65
Step-by-step explanation:
Max number
Min number
Answer:
Min: 31
Q1: 38
Median: 49
Q3: 52
Max: 65
Step-by-step explanation:
Min Number: 31
Max Number: 65
Use the figure to answer the following question.
1.3 m
0.5 m
2.4 m
What is the area, in square meters, of the figure?
O A. 0.78 square meters
OB. 0.6 square meters
C. 1.56 square meters
O D. 1.2 square meters
Answer:
The answer to the equation was c so yes you are right:)
y=3x/5-6 in standard form
Answer:
The standard form is 3x-5y-30=0
You have a cell phone plan that allows you 800 free minutes and 800 free texts. The base plan costs $55.00. Overage charges are 2 cents per extra minute and 2 cents per extra text message. If you use 899 minutes of talking and 905 text messages, what will be the cost of your bill?
Which figures can be precisely defined by using only undefined terms? Select three options.
angle
arc
circle
line segment
parallel lines
Answer:
Circle, angle, and line segment.
Gavin drew a circle with a circumference of 10π centimeters. Which best represents the area of Gavin's circle in square centimeters?
Answer:
78.5cm^2
Step-by-step explanation:
Circumference equation = 2πr with radius r
10π = 2πr so r = 10π/2π = 5
Area of circle = πr^2
π * 5^2 = π * 25 = 25π = 78.53981... = 78.5 cm^2
Find the range of the data in the box plot below."
rebounds
Juan's number of rebounds each game
+
HHH
0
3
+
12
6
9
15
Answer:
9
Step-by-step explanation:
Khan Academy
Milly wants to buy this seated Elliptical for 169.99 (regularly 250.00)
What's the discount? What will be the total price afterwards?
What is x? I’ll make you the brainliest
Answer:
48
Step-by-step explanation:
If EG=8, OE=4
x/12=4
x=4(12)
x=48