The number of hours, t, it takes a boat to travel 15 miles upstream is represented
by the given equation.
15
t=
r-c
Which equation represents the rate of the current, c, in terms of r, the rate of the
boat, and t?
A.
15 - rt
CE
15-16
BC=
rt - 15
c = - 7
C. C= -15+r+t
D. C = 15 -r-t
Answers
The equation of c is an illustration of subject of formula
The equation of c in terms of r and t is c = r - 15/t
How to determine the equation?The equation is given as:
t = 15/(r - c)
Cross multiply
t(r - c) = 15
Divide both sides by t
r - c = 15/t
Subtract r from both sides
-c = -r + 15/t
Multiply both sides by -1
c = r - 15/t
Take LCM
[tex]c = \frac{rt - 15}{t}[/tex]
Hence, the equation of c in terms of r and t is [tex]c = \frac{rt - 15}{t}[/tex]
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Related Questions
What is 1050 rounded to the nearest thousand?
Answers
Answer:
1100
Step-by-step explanation:
We round the number up to the nearest hundred if the last two digits in the number are 50 or above.
We round the number down to the nearest hundred if the last two digits in the number are 49 or below.
If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.
A bucket contains 3 small red blocks, 5 small yellow blocks, 5 large yellow and 7 large red blocks. If a block is drawn randomly, what is the probability that the block is yellow, given that it is one of the large yellow blocks
Answers
Answer:
probability = favorable cases / true cases
p(A)=5/20 simplified by 5 = 1/4
answer : the probability that the block is one of the large yellow it's 1/4.
A 10-speed bike changes gears by moving the chain to different size sprockets on the front and back. The speed at which the bike goes varies directly with the number of revolutions per minute (rpm) you turn the pedals, directly with the number of teeth on the front sprocket, and inversely with the number of teeth on the back sprocket. A standard bike with 70 cm diameter wheels will go about 7.4 kilometers per hour if you pedal 40 rpm in the lowest gear (39-tooth front sprocket, 28-tooth back one). Write an equation expressing km/h in terms of the three independent variables.
Answers
The variation is a joint variation, and the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]
How to determine the equation in terms of the variables?The direct and the inverse variations from the question can be represented using:
[tex]s = k\frac{rf}{b}[/tex]
Where:
s represents the speed; s = 10k represents the constant of variationr represents the number of revolutions per minutef represents the number of front sprocket teethb represents the number of back sprocket teethFrom the question, we have:
r = 40; f = 39; b = 28
So, we have:
[tex]s = k\frac{rf}{b}[/tex]
[tex]10 = k\frac{40 * 39}{28}[/tex]
Make k the subject
[tex]k = \frac{10 * 28}{40 * 39}[/tex]
Evaluate
k = 0.18
Substitute k = 0.18 in [tex]s = k\frac{rf}{b}[/tex]
[tex]s = 0.18\frac{rf}{b}[/tex]
Hence, the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]
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#6 You want to find out what type of pet is most commonly adopted from the shelter. Over the course of a month, you randomly survey 40 people who have just adopted a pet. Of those 40 people, 23 adopted dogs. If about 4,500 people adopt pets each year, about how many can you predict will dogs?
Answers
Answer:
we predict 2,587 persons will adopt dogs
Step-by-step explanation:
out of 40 persons 23 adopt dogs
Then
out of 40×25 persons 23×25 adopt dogs
Then
out of 1000 persons 575 adopt dogs
Then
out of 1000×4.5persons 575×4.5 adopt dogs
Then
out of 4,500 persons 2,587.5 adopt dogs
Method 2 :
Let x Ben the number of persons we predict they will adopt dogs:
Here we have a proportional relationship:
Then
[tex]\frac{4500}{40} =\frac{x}{23}[/tex]
[tex]\Longleftrightarrow x = \frac{4500\times 23}{40} =2587.5[/tex]
10 One of the legs of a right triangle has vertices with coordinates (-2,4) and (10,0).
What is the equation of the line of the other leg of the right triangle if it shares the vertice of (10,0)?
Answers
The equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3
How to find the equation of a line?The equation of a line in slope-intercept form is expressed as y = mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points (-2, 4) and (10, 0)
Find the slope
Slope = -4/12
Slope = -1/3
Determine the y-intecept
0 = -1/3(10) + b
b = 10/3
Determine the equation
y = -1/3x + 10/3
Hence the equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3
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A student wrote the following equations:
3y + 6 = 2x
2y - 3x = 6
The lines represented by these equations are
(1) parallel
(2) the same line
(3) perpendicular
(4) intersecting, but not perpendicular
Answers
Using linear function concepts, it is found that the two lines can be classified as:
(4) intersecting, but not perpendicular.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The slope defines if the lines are parallel or perpendicular, as follows:
If they are parallel, they have the same slope.If they are perpendicular, the multiplication of the slopes is of -1.If the multiplication of -1, and the slopes are different, they are intersecting.In this problem, the lines in slope-intercept formula are:
[tex]y = \frac{2}{3}x - 2 \rightarrow = m = \frac{2}{3}[/tex]
[tex]y = \frac{3}{2}x + 3 \rightarrow m = \frac{3}{2}[/tex]
Then:
[tex]\frac{2}{3} \times \frac{3}{2} = 1[/tex]
So they are intersecting and not perpendicular, which means that option 4 is correct.
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Given m||n find the value of x (x+ 20) (4x-5)
Answers
Answer:
x² + 80x - 5
Step-by-step explanation:
x (x+ 20) (4x-5)x [tex]*[/tex] x = x² x [tex]*[/tex] 20 = 20xx² + 20x [tex]*[/tex] 4x - 5 20x [tex]*[/tex] 4x = 80xso in all = x² + 80x - 5The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.
Answers
Answer:
(-13/6, -12)
&
(2, 13)
Step-by-step explanation:
x · y = 26 -------> x = 26/y
y = 1 + 6x
SUB for y
x(1 + 6x) = 26
x + 6x² = 26
SOLVE for x
6x² + x - 26 = 0
6x² + 13x - 12x - 26 = 0
6x(x - 2) 13(x - 2) = 0
(6x + 13)(x - 2) = 0
x = -13/6 or 2
Test x = -13/6 for both equations
Equation 1
-13/6 · y = 26
y = -156/13
y = -12
Equation 2
y = 1 + 6(-13/6)
y = 1 - 13
y = -12
-12 = -12 ✅
Test x = 2 for both equations
Equation 1
2 · y = 26
y = 26/2
y = 13
Equation 2
y = 1 + 6(2)
y = 1 + 12
y = 13
13 = 13 ✅
Hope this helps & God bless!
Walt collected random samples of data on the number of people who eat at who
restaurants daily. He created two dot plots to represent his data. Find the degree of
overlap and the mean of the two data sets. Write a paragraph, using the RACE
format, explaining how you got the answer.
Answers
The mean of the data sets of Restaurants A and B which Walt collected is 17.3 and 15.8 respectively. Degree of overlap of two data set is 1.5.
What is mean of data set?The mean of the data is the average value of the given data. The mean of the data is the ratio of sum of all the values of data to the total number of values of data.
Walt collected random samples of data on the number of people who eat at who restaurants daily. He created two dot plots to represent his data.
Restaurants A- 10,15,16,18,18,18,19,19,20,20Restaurants B- 10,13,15,15,15,16,17,18,19,20Mean of Restaurants A is,
[tex]X_A=\dfrac{10+15+16+18+18+18+19+19+20+20}{10}\\X_A=\dfrac{173}{10}\\X_A=17.3[/tex]
Mean of Restaurants B is,
[tex]X_A=\dfrac{ 10+13+15+15+15+16+17+18+19+20}{10}\\X_A=\dfrac{158}{10}\\X_A=15.8[/tex]
Degree of overlap is the difference of both the means.
[tex]DO=X_A-X_B\\DO=1.5[/tex]
Thus, the mean of the data sets of Restaurants A and B which Walt collected is 17.3 and 15.8 respectively. Degree of overlap of two data set is 1.5.
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A 30% discount on a
computer is $90. What was the
cost of the computer before the
discount?
Answers
Answer: $300 is the cost before the discount
Step-by-step explanation:
Divide $90 by 30% which = $300.
A team of researchers measured the length of 5 different rainbow trout pulled from different locations in a lake. length, in.: {18, 22, 15, 28, 17} what is the estimated mean absolute deviation of the lengths of rainbow trout in the lake? 1.3 in. 4 in. 20 in. 61 in.
Answers
4IN
Step-by-step explanation:
I took the test for k12 and got 100% hope it helps
Answer:
4 in
Step-by-step explanation:
18 + 22 + 15 + 28 + 17 = 100
100 / 5 = 20
So, the mean for the data set: 18, 22, 15, 28, 17 is 20.
18 - 20 = |2|
22 - 20 = |2|
15 - 20 = |5|
28 - 20 = |8|
17 - 20 = |3|
2 + 2 + 5 + 8 + 3 = 20
20 / 5 = 4
So, 4 in is the mean absolute deviation (MAD).
I also took the test.
It is common knowledge that a fair coin lands heads up 50% of the time and tails up 50% of the time. For fair coins, a probability of 0 is assigned to the coin landing on its edge. But what if several coins were glued together? A teacher claims that if 10 pennies were glued together and flipped many times, the penny stack would land on heads 25% of the time, tails 25% of the time, and on its edge 50% of the time. To investigate this claim, a student glues 10 pennies together and flips the stack 200 times. The student would like to know if there is convincing evidence that the distribution differs from what the teacher claimed. What are the appropriate hypotheses?
H0: The distribution of flips is 25% heads, 25% tails, and 50% edge.
Ha: The distribution of flips is not 25% heads, 25% tails, and 50% edge.
H0: The distribution of flips is not 25% heads, 25% tails, and 50% edge.
Ha: The distribution of flips is 25% heads, 25% tails, and 50% edge.
H0: The penny stack will land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.
Ha: The penny stack will not land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.
H0: The penny stack will not land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.
Ha: The penny stack will land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 tim
Answers
Answer:
The penny stack will land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times
Step-by-step explanation:
25% of 200=50
50% of 200=100
So, the coin will land 50 times on heads, 50 times on tails and 100 times on edge
Answer:
It's A on EDGE
Step-by-step explanation:
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams. A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams. Which metal has the greater density?
PLEASE SHOW WORK, WILL MARK BRAINLIEST
Answers
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams than has the greater density A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
How are density, volume and mass of a substance related?Suppose that a finite amount of substance is there having its properties as:
mass of substance = m kg
density of substance = d kg/m³
volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams.
[tex]d = \dfrac{73.92}{8.25}\\d = 8.96[/tex]
A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
[tex]d = \dfrac{39.35}{5}\\\\d = 7.87[/tex]
Thus, A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams than has the greater density A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
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26) Anjali and Rob are selling cookie dough for a school fundraiser. Customers can buy packages of
sugar cookie dough and packages of oatmeal cookie dough. Anjali sold 6 packages of sugar cookie
dough and 2 packages of oatmeal cookie dough for a total of $116. Rob sold 9 packages of sugar
cookie dough and 12 packages of oatmeal cookie dough for a total of $318. Find the cost each of
one package of sugar cookie dough and one package of oatmeal cookie dough.
Answers
Answer:
Sugar cookie dough packages cost 14 dollars each, and oatmeal cookie dough packages cost 16 dollars each.
Step-by-step explanation:
Let s equal the cost of a sugar cookie dough package, and o equal the cost of oatmeal cookie dough packages.
6s + 2o = 116
9s+12o = 318
therefore,
18s+6o = 348
18s+24o = 636
Subtracting them, we get -18o = -288, or 18o = 288
Therefore, o = 16, and 6s+32=116, so 6s=84, so s = 14
Need help with this homework question
Answers
A cylinder with height,h, and radius,r, has a volume of 1200pi cubic units. What could be the dimensions of this cylinder?
Answers
Answer:
h = 12 units, r = 10 units
Step-by-step explanation:
[tex]v=\pi (10)^{2} (12)=\pi (100)(12)=1200\pi[/tex]
Hope this helps
What is the area of each triangular base of the prism?
Answers
Each base: 12 ft^2
Surface Area: 48 ft^2
Explanation:Assuming it is a triangular prisim made of equilateral triangles, I would assume the formula would be 4 times the area of one triangular base, following the formula:
[tex]a = \frac{1}{2} bh \\ a = \frac{1}{2} (6)(4) \\ a = 12 \\ 4 \times 12 = 48[/tex]
Instructions: Find the measure of the indicated angle.
Answers
Answer:
x = 35
Step-by-step explanation:
As it is an isosceles triangle, two sides are equal (that's why we took two x)
2x = 180- 110
2x = 70
x = 70/2
x = 35
I hope my answer helps you.
The measure of the indicated angle is 35 degrees.
What is the angle sum property?
A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
We are given that;
Angle = 110degree
Now,
x+x+110=180
2x+110=180
2x=180-110
2x=70
x=70/2
x=35
Therefore, by the angle sum property of triangles the answer will be 35degree.
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What is the end behavior of f(x)=5x^3-2x+5
Answers
Answer:
A
Step-by-step explanation:
positive leading coefficient means increasing
The perimeter of a rectangular poster is 14 feet and the length is 4 feet. Describe how to use the perimeter formula to find the width.
Answers
Answer:
solve the equation with known values filled in; width is 3 ft.
Step-by-step explanation:
The perimeter formula can be used to find a missing value by filling in all of the known values, and solving the resulting equation.
__
P = 2(L +W) . . . . . . perimeter formula
14 = 2(4 +W) . . . . . known values substituted
7 = 4 +W . . . . . . . divide by 2
3 = W . . . . . . . . . subtract 4
The width is found to be 3 feet using the perimeter formula.
Answer:
The width of rectangular poster is 3 feet.
Step-by-step explanation:
As per given question we have provided that :
→ Perimeter of rectangle = 14 feet→ Length of rectangle = 4 feetWe need to find the width of rectangle.
Here's the required formula to find the width :
[tex]{\underbrace{\sf{\small{ \: \: P = 2(L + W) \: \: }}}}[/tex]
➟ P = Perimeter ➟ L = Length ➟ W = WidthCalculating the width of rectangular poster by substituting the values in the formula :
[tex]\begin{gathered} \qquad{\twoheadrightarrow{\sf{\small{ \: \: P = 2(L + W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: 14 = 2(4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: \dfrac{14}{2} = (4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: 7= (4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: W = 7 - 4\: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\underline{\underline{\small{ \: \: W = 3\: \: }}}}}} \end{gathered}[/tex]
Hence, the width of rectangular poster is 3 feet.
[tex]\rule{200}2[/tex]
The sum of two numbers is 21. The difference of the two numbers is 1. What are the two numbers?
Answers
Answer:
10 and 11
Step-by-step explanation:
10+11=21
11-10=1
1 apart, and they add to 21
I need help! This pattern repeats every 4 terms. The pattern is square, hexagon, trapezoid, triangle. What is the shape in the 7th term of this pattern?
Answers
==========================================================
Explanation:
There are two ways to do this problem.
Method 1 involves listing out the terms until we reach the seventh one.
squarehexagontrapezoidtrianglesquarehexagontrapezoidtriangleWe see that the trapezoid is term 7.
-------------
Method 2 is faster and the one I recommend.
Since the pattern repeats every 4 items, this means we divide by 4 and look at the remainder. Ignore the quotient entirely.
7/4 = 1 remainder 3
The remainder 3 means that the answer is found in term 3, which is the trapezoid.
find the circumference of the circle using 3.14 for pi
Answers
34.54
Explanation:
The hint states C=pid
D= diameter=11
Pi=3.14
C = (3.14)(11)
BOOM MUTI-LY THE 2 NUMBERS AND YOU GET YOUR ANSWER 34.54
Hope it helps, Let me know if you have any other questions !
Have a nice rest of your day :)
Answer: 34.54
Multiple 11 by 3.14 and you'll get 34.54
and if you need the radius just divide 11 by 2 and get 5.5
I hope this helps! :)
Find the AREA OF THE BASE of the
cylinder!
base is 10yd and height is 15yd
Answers
I assume that 10yards is the diameter of the base and so the radius in this question would
be 5 yards.
we plug in our numbers into the formula
A=5^2(pi)
A=25(pi)
and then into the calculator,
A= 78.54
Two yellow lines (one solid, another broken) in the center of a two-way road mean that vehicles traveling ___________.
Answers
This question has two parts. Use the figure to answer Part A and Part B.
Angle ABC is a right angle.
a
Part A
Which equation could be used to correctly solve for X?
А
O A. 2x = 56
O B. 2x+56 = 90
OC. 2x + 56 = 180
Part B
What is the value of x? Enter the answer in the box.
56°
(2x)
B
C
X=
* not drown to scale
Answers
Answer:
Pt 1) B
Pt 2) 17
Step-by-step explanation:
a right angle is 90 so 56 plus 2x should equal 90. Subtract 56 from 90 and get 34, because it's 2x you divide by 2 and get 17
Find the 7th term of the geometric sequence show below
7x, -7x^5, 7x^9,…
Answers
Answer:
7x^25 :)
Step-by-step explanation:
1: 7x,
2. 7x^5,
3. 7x^9,
4. 7x^13,
5. 7x^17,
6. 7x^21,
7. 7x^25
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
[tex]7x^{25}[/tex]
Step-by-step explanation:
Given sequence: [tex]7x, -7x^5, 7x^9[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
[tex]a_1=7x[/tex]
[tex]a_2=-7x^5[/tex]
[tex]a_3=7x^9[/tex]
To find the common ratio, divide one term by the previous term:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{-7x^5}{7x}=-x^4[/tex]
Therefore, substituting the found values of a and r into the formula:
[tex]\implies a_n=(7x)(-x^4)^{n-1}[/tex]
To find the 7th term, substitute n = 7 into the formula:
[tex]\begin{aligned}\implies a_7 & =(7x)(-x^4)^{7-1}\\ & = (7x)(-x^4)^6\\ & = (7x)(x^{24})\\ & = 7x^{25}\end{aligned}[/tex]
what expressions are equvilent to 9x^{2} - 256
Answers
Answer:
(3x + 16)(3x - 16)
Step-by-step explanation:
[tex]9 {x}^{2} - 256 \\ \\ = {(3x)}^{2} - {(16)}^{2} \\ \\ = (3x + 16)(3x - 16)[/tex]
Judy simplified the expression (3x+1)(x-3) -( 2-2x^2-3x)
Answers
How many different vacation combinations do you have to choose from?
Answers
Answer:
12 different vacation caombinations
Step-by-step explanation:
has 3 options of Theme Park and 4 options of length of trip
[tex]C=(3)(4)=12[/tex]
Hope this helps