Taking into consideration the upstream and downstream speed, and the equal time taken to travel upstream and downstream distance, the speed of the boat in the still water is found out to be 10mph.
It is given to us that -
The speed of the river current = 2mph
Time taken for the boat to travel 30 miles downstream = Time taken for the boat to travel 20 miles upstream --- (1)
We have to find out the speed of the boat in still water.
Let us say that the speed of the boat in still water is x mph.
We know that -
Speed = Distance/Time
=> Time = Distance/Speed ----- (2)
When travelling upstream, the boat is slower and thus, we subtract speed of the current from the speed of the boat.
When travelling downstream, the boat is faster as it goes with the current and thus, we add the speed of the current with the speed of the boat.
From equation (1), we have
Time to travel 30 miles downstream = Time to travel 20 miles upstream
[tex]= > \frac{30}{x-2} =\frac{20}{x+2} \\= > 30(x+2)=20(x-2)\\= > 30x+60=20x-40\\= > 10x=100\\= > x=10[/tex]
Thus, taking into consideration the upstream and downstream speed, the speed of the boat in the still water is 10mph.
To learn more about upstream of a river visit https://brainly.com/question/5057152
#SPJ1
Someone please help step by step how to solve
3(x+2)-5=13
pls
Ira invests $4000 into an account that earns 0.6% simple interest annually. Which statement best describes the relationship between the number of years Ira has his money invested and the balance in any year
The Amount of money that she received at the end of the read is $4024, the relationship between the number of years Ira has his money invested and the balance in any year differs by $24 which is the simple interest.
Amount invested by Ira = P = $4000
The rate of Interest (r) = 0.6 %
Time period (t) = 1 year.
The simple interest is given by,
[tex]S.I. = \frac{P*r*t}{100}[/tex]
Now, putting the values in the formula, we get:
[tex]S.I. = \frac{4000*0.6*1}{100} =24[/tex]
Hence, the simple interest will be $24
Now, the Amount/balance that she received in the year is A = P +S.I
A = P+S.I.
A = 4000 +24 = $4024
To read more about simple interests, visit https://brainly.com/question/25663053
#SPJ1
Answer:
The relationship is linear. His account increases each year by a constant value of $24.
Step-by-step explanation:
took the test
A rock falls from a tower that is 360 feet high. As it is falling, its height is given by the formula ℎ= 200 −162. How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth of a second.
The time it will takes for the rock to hit the ground (h=0) given the height of 360 feet high is 3.53 seconds.
What is the time of falling?The concept that will be used in the calculation is the concept of height and time .
The formular for the expression is given as ℎ= 200 −16t^2
Then the height of the tower is been given as 360 feet high
ℎ= 200 −16t^2
then
t^2=200/16
t^2=12.5
t=3.53 seconds
Find out more on Height at https://brainly.com/question/12446886
#SPJ1
Which parts of the triangles are congruent in the image?
Answer:
B, C, E
Step-by-step explanation:
B is correct because it is written to the side and also because of the Definition of midpoint.
C is correct because HL and KI H and I are congruent just like L and K because of alternate interior angles.
E is correct because of the verticle angle theorum.
x + y is greater than or equal to 4
Answer:
I am going sujshsbeba170
If the 21st and 22nd terms in the expansion of(1+x)⁴⁴ are equal find the value of x
Answer:
21st 22nd are equal so ×=0
please help it is urgent
[tex]\frac{6x + 1}{6x - 4} - \frac{47 - 27 {x}^{2} }{5 {x}^{2} - 24} = \frac{5}{6} [/tex]
solve x
Answer:
Soultion\left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right)\quad :\quad x=-\frac{7+\sqrt{253}}{6},\:x=\frac{\sqrt{253}-7}{6} steps \left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right) simplify -2x^2-\frac{14x}{3}+\frac{34}{3}=0.
Step-by-step explanation:
I got you my boy.
a) What are the coordinates of A?
b) What are the coordinates of B?
Answer:
coordinates of A are (-4.5, 2)
coordinates of B are (0, -3.5)
7/15 - 6 2/5 = need the answers
The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
Given,
In the question:
The Fraction is given as:
7/15 - [tex]6\frac{2}{5}[/tex]
To solve the above fraction.
Now, According to the question;
Let's know
What is fraction in math?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.
Come to the question:
7/15 - [tex]6\frac{2}{5}[/tex]
7/15 - 32/5
Take the L.C.M
= [tex]\frac{7-96}{15}[/tex]
= -89/15
Hence, The fraction solve 7/15 - 6 2/5 , we get the answer -89/15.
Learn more about Fraction at;
https://brainly.com/question/10354322
#SPJ9
The following data are for Jay Robert Company. Breakeven sales revenue $250,000 Fixed costs $150,000 Calculate the sales revenue necessary to generate net income of $100,000. $618,667 $533,333 $625,000 $400,000 $416,667
The sales revenue necessary to generate net income of $100,000 is: $416,667.
How to find the sales revenue?Using this formula to find the sales revenue
Sales revenue = Sales revenue + (Sales revenue × Net income / Fixed costs)
Let plug in the formula
Sales revenue = $250,000 + ($250,000 × $100,000 /$150,000)
Sales revenue = $250,000 + ($250,000 ×0.6666666)
Sales revenue = $250,000 + $166,666.65
Sales revenue = $416,666.65
Sales revenue = $416,667 (Approximately)
Therefore the correct option is E.
Learn more about sales revenue here:https://brainly.com/question/28390695
#SPJ1
7p5 · 4p3 I have no idea how to do this please help
Lamar buys candy that costs $5 per pound. He will buy at most 12 pounds of candy. What are the possible amounts he will spend on candy
Use C for the amount (in dollars) Lamar will spend on candy.
Write your answer as an inequality solved for C.
Answer:
He will spend $60 on candy
Step-by-step explanation:
If the cost for one pound is $5, then just multiply.
12 x $5 = $60
Answer: C=7
Step-by-step explanation: C=12+5
the answer is c=7
Can you help me please and explain I don’t get this. *slope*
Answer:-5/1
Step-by-step explanation:
down 5 and over 1
to get the slope, find a spot on the graph and then go 1 to the right and read how much the graph went up or down.
on 5) you see it did neither, so m=0
when the graph goes up, m is positive, when it goes down, m is negative.
so on graph 1, you have 2 dots.
you go 2 right, and 4 down. when the dots are not 1 apart (counting going right) then divide by the steps you went right.
4 divided by 2 is 2.
-> graph went down, slope for 1) is m = -2
graph 2) you go 2 right and 2 up, 2/2 = 1. you went up, so m is positive and m = 1 for this graph.
3) is undefined because it doesn't go anywhere when you go right, it's 100% vertical
4) m = -5 because you went 1 right and 5 down
5) you go 6 right between the dots and 4 down. m is negative because it went down, not up. so m = -(4/6)
Where does 1/6 land on a number line
Answer:
On a number line, 1/6 would land in the exact middle between 0 and 2/6
Step-by-step explanation:
Not too sure what your question meant, but I hope my answer helped!
If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)
Please help an 8th grader in needdddddddddddddddddddddddddddddddddddddddddddd
Answer:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Step-by-step explanation:
From a fellow 8th grader <3
First, let's review the slope of a line: y = mx + b
Where m is the slope, and b the y-intercept
Let's find the slope. To do this I will select 2 points from this graph, and using the slope formula I will calculate it
Slope formula: [tex]\frac{rise}{run} =\frac{change- in- y}{change-in-x} =\frac{y^2-y^1}{x^2-x^1}[/tex]
To get the most accurate answer, I will be using the 2 points given that are directly on the line:
1 = (2, 30)
2 = (4, 10)
Slope: [tex]\frac{10-30}{4-2} =\frac{-20}{2} =-10[/tex]
m = -10
It makes sense that it is a negative, since the graph continues downwards.
Let's update our equation: y = -10x + b
We can see that the line intersects the y-axis at y = 50
Plug this into our b-value:
y = -10x + 50
Now, I would recommend using a graphing calculator (like a TI-83) or an online one (like desmos) to double check this. I have attached a screenshot of this line on desmos. From there we can see if this line matches up with the one seen on your graph.
Our answer is:
The two points used to find the slope:
[tex]x_1,y_1[/tex]: 2,30
[tex]y_1,y_2:[/tex] 4,10
Final equation: y = -10x + 50
Please let me know if this helped you, and if this was the correct answer! If it is incorrect I will do my best to revise my answer.
Answer: y intercept is (0,50) and Slope is -10.
Final equation is y= -10x+50
Step-by-step explanation:
Y-intercept is at what point the line intercepts the y-axis. It intersects at (0,50) coordinate point as you can see.
Slope is change in y divided by the change in x. When you change x by 1, y changes by -10. So it is -10/1 = -10. Slope is -10.
Since we know y intercept and slope equation is y=-10x+50
juan thinks the answer is between 5 and 6 melanie says the answer is between 3 and 4 who is correct [tex]\sqrt[3]{28}[/tex]
Answer:
28
Step-by-step explanation:
4,8,12,16,20,24,28. +4 every time
What is the slope of a line perpendicular to the line whose equation is 5x-y=-7. Fully simplify your answer.
Answer:
-1/5
Step-b-1/5y-step explanation:
The rule for a perpendicular slope of a line is -1/s
In this case, we find the slope of the line first.
5x - y = -7
-y = -5x - 7
y = 5x + 7
The slope is 5, so -1/(5) is the slope of the perpendicular line.
Please help I was sick and missed out on class.Thank you
Answer: [tex]\frac{0}{24}[/tex]
Step-by-step explanation:
The slope is [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex], or reverse: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
If we substitute, we get that [tex]\frac{2-2}{6-(-18)}[/tex].
Simplify to get [tex]\frac{0}{24}[/tex].
se the distributive property to find an expression that is equivalent to 42x + 12 .
The equivalent expression using the distributive property is 6(7x + 2)
How to determine the equivalent of the expressions?From the question, we have the following expression
42x + 12
Rewrite the given expression as follows
This is represented using
(42x + 12)
Factor out 2 from the expression
So, we have the following representation
42x + 12 = 2(21x + 6)
Factor out 3 from the expression
So, we have the following representation
42x + 12 = 2 * 3(7x + 2)
Evaluate the products
42x + 12 = 6(7x + 2)
The above represents the equivalent expression
Read more about GCF at
brainly.com/question/28552398
#SPJ1
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
24.359
Step-by-step explanation:
The height is opposite of the 77 so we are using sin. The length of the ladder is the hypotenuse.
sin(77°)=height/25 Set up equation sin=height/hypotenuse
25*sin(77°)=height Multiply both sides by 25
25*.96437=height
height=24.359
Solve each equation below. Show each step and check your work.
a) 56a – 178 = 98 – 248
b) 640 + 70 = 69y + 20
Answer:
A) 0.5
B) 10
Step-by-step explanation:
A) First, you need to Combine Like Terms on the right side of the =
98-248 = -150
Now, you need to Isolate the variable by getting rid of the -178. What you do to one side, you must do the the other.
56a-178(+178) = -150(+178)
56a = 28
Finally, you must remove that 56 on the a. Since it stands for 56 x a, you must do the same you did with the -178 except with Division.
56a/56 = 28/56
a = 0.5
B) Combine Like terms
640+70 = 710
Isolate the variable
710(-20) = 69y+20(=20)
690 = 69y
Remove the 69 with division
690/69 = 69y/69
10 = y
The simple interest on a sum of money invested 6 months at 5% per annum is $1680. Determine the amount of money invested.
Answer:
9514 1404 393
Answer:
$67,200
Step-by-step explanation:
The amount if interest is given by the formula ...
I = Prt
where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.
P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025
P = $67,200
The amount invested was $67,200.
Step-by-step explanation:
8. In the following diagram, the diameter of the circle is 15m. What is the distance between the chord and the edge of the circle?
Answer:
7
Step-by-step explanation:
15-8
-1.25 + 2 1/5 + (-3.5)
Answer: -2.55
Step-by-step explanation:
Answer:
-2.55
Step-by-step explanation:
-1.25 + 2 1/5 + (-3.5) =
= -1.25 + 2.2 - 3.5
= 0.95 - 3.5
= -2.55
If a bar of soap cost 70p and a box of plasters cost 95p how much does buying one of each cost
The cost of buying one of each of the soap and plaster is 165p.
How to calculate the cost?From the information, the bar of soap cost 70p and a box of plasters cost 95p.
It should be noted that in order to find the total cost, we will have to add the. oat of each product.
This will be:
Total cost = Cost of soap + Cost of plaster
= 70p + 95p
= 165 p
The cost is 165p.
Learn more about cost on:
brainly.com/question/25109150
#SPJ1
what is 33+900212323
Answer:
900212356
Step-by-step explanation:
Select two numbers that multiply together to make 1 million.
40 A
2,000 B
5,000 C
25,000 D
Answer: A and D
Step-by-step explanation: 40 x 25,000 = 1,000,000
Answer: A and C
Step-by-step explanation:
Because 40x25000 equals 1 million
Perform the following operation. Write the answer in scientific notation.
0.008/40,000
(Use the multiplication symbol in the math palette as needed.)
Answer:
8.0 × 10^-3 ÷ 4.0 × 10^4
= 2.0 × 10^-3-4
= 2.0 × 10^-7
or 0.0000002
Need help with question
A board game uses the deck of 20 cards shown to the right. Two cards are selected at a random from this deck. Calculate the probability that first card selected has a yellow bird and second cared selected has a lion both with and without replacement
The probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement is 1/40 and 1/38. respectively.
What is probability?
Probability is the likelihood of an event or more than one event occurring. It is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Probability may also be described as the likelihood of an event occurring divided by the number of expected outcomes of the event. i.e.,
P(A) = f / N
Where:
P(A) = Probability of an event (event A) occurring
f = Number of ways an event can occur (frequency)
N = Total number of outcomes possible
Here deck of 20 cards are given which implies total number of possible outcomes are 20. From these 20 cards 5 cards has lions and 5 cards has birds in which 2 are yellow and 3 are red.
Now two cards are selected randomly.
We have to find the probability that first card selected has a yellow bird and second card selected has a lion both probability that first card selected has a yellow bird and second card selected has a lion both with and without replacement.
Probability with replacement:
Probability that first card selected has a yellow bird = 2/20 ---(1)
Since replacement is allowed so the probability that second card selected has a lion = 5/20---(2)
So, the probability that first card selected has a yellow bird and second card selected has a lion with replacement = (1) * (2) = 2/20 * 5/20 = 1/40.
Probability without replacement:
Probability that first card selected has a yellow bird = 2/20 ---(3)
And since replacement is not allowed, the probability that second card selected has a lion = 5/19---(4)
So, the probability that first card selected has a yellow bird and second card selected has a lion without replacement = (3) * (4) = 2/20 * 5/19 = 1/38.
Therefore, the probability with and without replacement is 1/40 and 1/38. respectively.
To learn more about probability, visit
https://brainly.com/question/12705780
#SPJ1