The rate of paddling in still water is 3 times than the speed of the current.
What is Speed?
The formula for the speed is calculated as;
Speed = Distance / Time
Given that;
Jennifer can paddle a certain distance with the current in 2.5 hr.
And, To cover the same distance against the current, she takes 5 hr.
Let distance be D , speed is S and the current speed will be C.
The we can formulate two conditions as;
(S + C) × 2.5 = D .... (I)
And, (S - C) × 5 = D .... (II)
Solve equation (i) and (ii) we get;
S = 3C
Thus, we can say that;
The rate of paddling in still water is 3 times than the speed of the current.
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The distance between city hall and the post office is 6 1/2 miles . The library site is 1 1/4 closer to city hall than to post office
City hall to post office = 6 1/2 miles
City hall to library site = 1 1/4 miles
library site to post office = unknown. let it be x. 5 1/4 miles
1 1/4 miles + x = 6 1/2 miles
x = 6 1/2 miles - 1 1/4 miles
Find x.
1) convert the mixed fractions into fractions. 6 1/2 = 13/2 ; 1 1/4 = 5/4
x = 13/2 - 5/4
2) get the common denominator. 4 is twice as much as 2. multiply 13/2 by 2/2
13/2 * 2/2 = 26/4
3) Subtract the top numbers and put over the same denominator
x = 26/4 - 5/4 = (26-5) / 4 = 21 / 4
4) simplify the fraction
x = 21/4 = 5 1/4 miles from library site to post office.
A room has an area of 60 square meters and a perimeter of 32 meters. What are the length and width of the room?
The length of the room is 10 m and width is 6m.
We have given that the area is 60 square meters
and perimeter of the square is 32 meters
What is the formula for the area of the square?[tex]Area =L \times W[/tex]
we have given that the area is 60
Therefore,[tex]L \times W = 60.......(1)[/tex]
What is the formula for the perimeter?[tex]Perimeter=2(L + W)[/tex]
From given we get,
[tex]2(L + W) = 32[/tex]
[tex]L + W = 16[/tex]
[tex]L = 16 - W.......(2)[/tex]
Substitute the value of L = 16 - W into (1) we get,
[tex]L \times W = 60[/tex]
[tex](16 - W) \times W = 60[/tex]
[tex]16W -W^2 = 60[/tex]
[tex]W^2 - 16W + 60 = 0[/tex]
[tex](W - 6)(W - 10) = 0[/tex]
[tex]W - 10 = 0\implies W = 10\\W - 6 = 0\implies W = 6[/tex]
Therefore the length is 10 m and width is 6m.
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The sum of three consecutive odd numbers is 111. What is the smallest of the three numbers? (Use 8 steps to success)
Angle x measures 110 degrees. If angle x is rotated 60 degrees what is the measure of angle x
tony buy 3 packages of gum. each package has 5 packs of gum.each pack of gumhas 10 pieces in it how many pieces of gum are in all three packages
Tony has a total of 150 pieces of gum in three packages, calculated by multiplying the number of packages (3) by the number of packs per package (5) and the number of pieces per pack (10).
To calculate the number of pieces of gum Tony has in all three packages, we need to multiply the number of packages by the number of packs in each package, and then by the number of pieces in each pack. First, we have 3 packages and each package contains 5 packs of gum. So, the total number of packs in the three packages is:
3 packages * 5 packs per package = 15 packs of gumNext, each pack has 10 pieces of gum, so the total number of pieces of gum in all the packs is:
15 packs of gum * 10 pieces per pack = 150 pieces of gumTherefore, Tony has a total of 150 pieces of gum in the three packages.
John’s teacher gave him the following system of equations and asked him to find the point of intersection.
5x + 7 = y
9x – 5= y
Select the ordered pair that represents the intersection of the lines represented by the two equation.
A.(3, –8)
B.(3, 22)
C.(5.5, 44.5)
D.(5.5, 34.5)
Write the ratio 3:101 as a fraction, decimal, and percent
what does the expression 5n represent
Calista has 4 one-dollar bills, 2 five-dollar bills, and 3 ten-dollar bills in her wallet. If she randomly chooses two bills, what is the probability that both of them are five-dollar bills?
The probability that Calista randomly chooses two five-dollar bills from her wallet is 1/36.
To calculate the probability of Calista choosing two five-dollar bills from her wallet, we start by determining the total number of ways she can choose two bills from her wallet, regardless of their denomination. Calista has a total of 9 bills (4 ones, 2 fives, and 3 tens), so the total number of ways to choose two bills is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.
The total number of ways to choose 2 bills from 9 is C(9, 2) = 9! / (2!(9-2)!) = 36. Next, we need to find the number of ways to choose 2 five-dollar bills from the 2 she has, which is simply C(2, 2) = 2! / (2!(2-2)!) = 1. The probability that both bills are five-dollar bills is then the number of ways to choose 2 fives divided by the total number of ways to choose any 2 bills, or P(both fives) = 1 / 36.
-2(4-3x)-6x=10 solve for x
an apple has a mass of 297 how many killo grams is it
My sister is 3 times as old as I am. Five years from now, she will be twice as old as I will be. How many years old is my sister now?
What percent of 90 is 36
At noon the temperature was 12°. It rose 8° during the afternoon, then dropped 28°by midnight. What was the temperature by midnight?
The temperature by midnight will be 32°.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Temperature is the randomness of the molecules known as temperature.
At noon the temperature was 12°.
It rose 8° during the afternoon, then dropped 28°by midnight.
Then the temperature by midnight will be given as,
⇒ 12° - 8° + 28°
⇒ 32°
Thus, the temperature by midnight will be 32°.
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What is the explicit rule for this geometric sequence?
a1=23;an=9⋅an−1
an=9⋅(23)n
an=23⋅9n
an=9⋅(23)n−1
an=23⋅9n−1
The Information about Geometric sequence is:
[tex]a_{1}=23 , a_{n}=9\times a_{n-1}[/tex]
→nth term of sequence = 9× (n-1) th term
Also , Common Ratio of a Geometric Sequence =[tex]\frac{\text{Second term }}{\text{First term}}[/tex]
[tex]\frac{a_{n}}{a_{n-1}}= \text{Common ratio}}=9\\a_{n}= a_{1}\times r ^{n-1}\\\\a_{n}=23\times 9^{n-1}[/tex]
Option 4 : [tex]a_{n}= 23 \times 9^{n-1}[/tex] is true.
The sketches below show cat's and Fred's driveways. If the perimeter of each others of their driveways is the same, what is the length and width of Cat's driveway?
Answer:
40,12
Step-by-step explanation:
u count how many x's u have.4(for the first square)
add up the regular numbers
so u should have4x+50
repeat for the second one
so u should have 4x+25=6x+20
solve
u get 2x=30 simplify
u get 15
now plug it in and there is ur answer
The value of length and width for Cat's driveway are 25 ft and 7.5 ft respectively.
What is a rectangle?A rectangle is a type of parallelogram having equal diagonals.
All the interior angles of a rectangle are equal to the right angle.
The diagonals of a rectangle do not bisect each other.
Given that,
The length and width of Cat's driveway are 25 ft and x ft respectively.
And, the length and width of Fred's driveways are 2x ft and x + 10 ft respectively.
The perimeter of a rectangle is given as,
2(l + b)
Substitute the values to obtain the perimeters as,
Perimeter of Cat's driveway = 2( x + 25) ft
And, perimeter of Fred's driveway = 2(2x + x + 10) ft.
As per the question,
2( x + 25) = 2(2x + x + 10)
=> ( x + 25) = (2x + x + 10)
=> x = 15/2
= 7.5
Hence, the length and width of Cat's driveway are 25 ft and 7.5 ft respectively.
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Hannah travels 6 times as many minutes to work as Raoul does. Together, they travel for 63 minutes. How many minutes does Hannah ? Draw a model and write an equation to solve. Also just tell me the strategys to draw the model thank you!
Write 2/3 of 4 as a fraction.
What is a scale drawing and how do you solve it? ( You can use any example to represent how to solve a scale drawing) Thanks!
-nana-
I still need help on this question
Imagine working with a younger sibling or student who is having trouble with the 9 times table. Create an algorithm to help the student learn how to do this easily. You may need to use outside resources to help you. If you do, make sure to document where you retrieved those sources.
Note: Remember an algorithm is a description on how to perform a process. Try using numbered steps or bullet points to list instructions. Your algorithm must be able to be easily followed by others so they get the same results as you did. For example, if you made an algorithm on how to make a chocolate cake, you'd want others to be able to follow it so that their cake ended up tasting as delicious as yours!
Describe your algorithm in the space provided below.
What is the answer I need to know
The tax on a property with an assessed value of $120,000 is $300. Find the tax on a property with an assessed value of $140,000
Find the value of the ratio for 63:135
Does this relation represent a function
Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.
If a linear equation is written in form y=1/2x-2, which method could be used to graph the line represented by the equation?
The linear equation y=1/2x -2 can be graphed by first plotting the y-intercept, then using the slope to plot additional points.
Explanation:Such equations can be graphed using a few different methods. One common approach is plotting data pairs on a coordinate grid.
For the given equation y = 1/2x - 2, it is convenient to begin by identifying b, which is the y-intercept. In our case, b equals -2. This is the point where the line crosses the y-axis. Next we need to understand what the slope (1/2 in our equation) means: for every step we move to the right along the x-axis (in the positive direction), we move half a step up along the y-axis.
To graph the equation, you start at the y-intercept (0,-2) and use the slope to identify subsequent points. For instance, if x = 2, then y = 1/2*2 - 2 = -1. Repeat this process with different x-values to plot enough points, and then connect them to draw the line written by the equation.
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Is y=6x-6 direct proportion
which is greater 0.7 or 3/4
The value of fraction 0.7 is greater than the value of 3/4.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the terms are 0.7 and 3/4. The values in the chemical points are,
First = 3/4 = 0.42
Second = 0.7
Here 0.7 is greater than the value 3/4 = 0.42
Hence, the greater value between the two values 3/4 and 0.7 is 0.7.
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how would i create a real life example that can be modeled by the expression -2×4