The rate of the cabin cruiser in calm water is 9 mph and the rate of the current 3 mph
Step-by-step explanation:
Given:
Speed of cabin cruiser travelling with then current = 12 mi in 1 h.
Against the current, it took 2 h to travel the same distance.
To Find:
The rate of the boat in calm water and the rate of the current = ?
Solution:
Let boat speed in calm water be s
Let rate of the current be c
Then
(s-c) = effective speed upstream
and
(s+c) = effective speed downstream
Writing a distance equation for each trip:
distance = [tex]time \times \text{effective speed}[/tex]
1(s + c) = 12
2(s - c) = 12
On the first equation divide both sides by 1
On the second equation divide both sides by 2
s + c = 12
s - c = 6
Now addition of the above two equations gives
2s = 18
s = 9 mph, boat speed in calm water
Lets substitute s value to find c value
s + c = 12
9 + c = 12
c = 12 - 9
c = 3 mph is the current
Final answer:
The cabin cruiser's rate in calm water is 9 mph, and the rate of the current is 3 mph.
Explanation:
To solve this problem, we will let c represent the rate of the current and r represent the rate of the cabin cruiser in calm water. When traveling with the current, the effective speed of the cruiser is r + c, and against the current, it is r - c.
Using the given information:
With the current: 12 miles in 1 hour means the speed with the current is 12 mph. So, r + c = 12.Against the current: 12 miles in 2 hours means the speed against the current is 6 mph. So, r - c = 6.Now we can set up a system of equations:
r + c = 12r - c = 6Adding these two equations, we get:
2r = 18
Dividing both sides by 2, we find r = 9 mph. Thus, the rate of the cabin cruiser in calm water is 9 mph. To find the rate of the current, plug r = 9 into either of the original equations. Let's use equation (2):
9 - c = 6
Subtracting 9 from both sides, we find c = 3 mph. So the rate of the current is 3 mph.
A rectangle has a length of 10 inches and a width of 8 inches
What is the approximate value of ? Round your answer to the nearest hundredth. 1.25 3.00 3.75 4.25
Option C:
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]
Solution:
Given expression:
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]
Summation means sum of the numbers.
Put n = 1 to 5 and sum all the numbers.
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex]
[tex]=3(0.2)^{1-1}+3(0.2)^{2-1}+3(0.2)^{3-1}+3(0.2)^{4-1}+3(0.2)^{5-1}[/tex]
[tex]=3(0.2)^{0}+3(0.2)^{1}+3(0.2)^{2}+3(0.2)^{3}+3(0.2)^{4}[/tex]
Using exponential rule: [tex]a^0=1[/tex], so that [tex]0.2^0=1[/tex]
[tex]=3(1)+0.6+0.12+0.024+0.0048[/tex]
[tex]=3.7488[/tex]
= 3.75
[tex]\sum_{n=1}^{5} 3(0.2)^{n-1}=3.75[/tex]
Option C is the correct answer.
Hence approximate value of [tex]\sum_{n=1}^{5} 3(0.2)^{n-1}[/tex] is 3.75.
Answer:
C
Step-by-step explanation:
edge
Is 24/40 4/5 a true proportion?
Answer:
no
Step-by-step explanation:
24 x 5 = 120
40 x 4= 160
Find the slope of a line that goes through (3,-9) and (5,-1)
evaluate the expression 3(x-1)2nd power +2x-7 for x=3
What is the first step for evaluating this expression?
Substitute 3 for X
distribute the 3
combine like terms
Answer:
11
3Step-by-step explanation:
Given
3(x - 1)² + 2x - 7 ← substitute x = 3 into the expression
= 3(3 - 1)² + 2(3) - 7
= 3(2)² + 6 - 7
= 3(4) - 1
= 12 - 1
= 11
The first step in evaluating the expression is to substitute 3 for x.
The first step in evaluating the expression 3(x-1)^2 + 2x - 7 for x=3 is to substitute 3 for x. This is because before you can simplify or combine like terms, you need to know the value of the variables involved. Once substitution is done, you can proceed with further simplification such as distributing and combining like terms.
an average Scott makes a basket 9 times out of 12 when he is practicing how many baskets can he expect to make when he tried 200.
Answer:
150
Step-by-step explanation:
We know that Scott's ratio of making the basket is 9/12. All we need to do is find out how many baskets he'll make if he attempts 200 shots.
So, 9/12 needs to become x/200. We don't know what x is yet, but there's a shortcut.
9/12 can be simplified by dividing 3 on the top and bottom.
9/12 ÷ 3/3 = 3/4
We can then see how many times 4 can go into 200.
200/4 = 50
So, we multiply 3/4 by 50 on both the top and bottom.
3/4 × 50/50 = 150/200.
So, if he attempts 200 shots then he'll make 150 of them.
Scott can expect to make approximately 150 baskets if he attempts 200 shots with his success rate being 9 out of 12, which equates to a 75% success rate.
Explanation:The question asks how many baskets Scott can expect to make if he tries 200 shots given that his average success rate is 9 out of 12. To find the answer, we can set up a proportion because Scott's shooting is a matter of probability and ratios. First, we determine Scott's success rate as a fraction: 9/12 which simplifies to 3/4 or a success rate of 75%.
Then, we apply this success rate to the new number of attempts (200) to find the expected number of successful baskets:
Expected number of baskets = Success rate x Total attemptsExpected number of baskets = (3/4) x 200Expected number of baskets = 150Therefore, if Scott attempts 200 shots, he can expect to make approximately 150 baskets.
Which expression means 9.7 split into a certain number of equal parts?
9.7n
9.7 + n
9.7 minus n
StartFraction 9.7 over n EndFraction
Answer:
Option D
Step-by-step explanation:
Just took the quiz :)
Answer:
it is the last answer
Step-by-step explanation:
How much simple interest will be charged on a 40,000 loan with a 7% interest rate that is paid back in 4 years?
Answer:$11200
Step-by-step explanation:
I = prt
I = 40,000( .07)(4)
I = $11200
What is 3 divided by 1773
The answer is 591 to the problem.
Which term completes the product so that it is the difference of squares?
| (-5x-3)(-5x+_
.
..
со со
Answer:
3
(-5x - 3)(-5x + 3)
Step-by-step explanation:
Difference of squares is a special type of factoring when you are subtracting two numbers that are perfect squares. Perfect squares are numbers that, when you find its square root, it is a whole number.
Difference of squares follows this rule:
a² - b² = (√a² - √b²)(√a² + √b²) = (a - b)(a + b)
Notice in the factored form, you take the same number in both brackets. In one set of brackets you add the numbers. In the other brackets, you subtract the numbers.
In (-5x - 3)(-5x + __), the blank in the second bracket will use the same number as the second number in the first brackets.
(-5x - 3)(-5x + 3)
Crispy Clover, a popular vegetarian restaurant, introduced a new menu that has 20\%20%20, percent more dishes than the previous menu. The previous menu had DDD dishes.
Which of the following expressions could represent how many dishes Crispy Clover's new menu has?
Question:
Crispy clover, a popular vegetarian restaurant, introduced a new menu that had 20% more dishes than the previous menu. The previous menu had D dishes. Which of the following expressions could represent how many dishes crispy clovers new menu has?
Answer:
The expression could represent how many dishes crispy clovers new menu has is:
[tex]D + \frac{1}{5}D \text{ or } 1.2D[/tex]
Solution:
Given that,
The new menu had 20% more dishes than the previous menu
The previous menu had D dishes
Therefore,
Previous menu = D dishes
New menu = 20 % more dishes than previous menu
Which means,
New menu = 20 % of previous menu + previous menu
Therefore,
New menu = 20 % of D + D
Solve the above equation
[tex]New\ menu = 20 \% \times D + D\\\\New\ menu = \frac{20}{100} \times D + D\\\\New\ menu = 0.2 \times D + D\\\\New\ menu = 0.2D + D = \frac{D}{5} + D = 1.2D[/tex]
Therefore, new menu has 1.2D dishes
jamie has 8/10 of a candy bar leftover he want to split into 1/3 pieces how many 1/3 pieces can he make
Answer:
Step-by-step explanation: solution.. 8/10 of candy bar left over to be split into 1/3 pieces...
(8/10)÷1/3=12/5=2.4pieces
A musicians hair was originally 11 2/3 inches long. She asked her hair dresser to cut off 5/8 of it off. How many inches did she have cut off?
Answer:
Step-by-step explanation:87
87
Which relationship describes angles 1 and 2?
Select each correct answer.
supplementary angles
adjacent angles
vertical angles
complementary angles
Answer:
it's supplementary angles
Step-by-step explanation:
1 + 2 =180
is y-4=2(x-2) and 4x-2y=5 perpendicular
Answer:
Therefore,
Slopes are Equal, Hence the Lines are not Perpendicular.
Step-by-step explanation:
Given:
[tex]y-4=2(x-2)=2x=-4\\\\y=2x[/tex] .......Equation ( 1 )
[tex]4x-2y=5\\2y=4x-5\\\\y=2x-\dfrac{5}{2}[/tex] .......Equation ( 2 )
Comparing with,
[tex]y=mx+c[/tex] ......General Slope point form
Where m =slope
We get
[tex]Slope = m1 = 2[/tex] For Equation ( 1 )
[tex]Slope = m2 = 2[/tex] For Equation ( 2 )
Hence,
[tex]m1=m2[=2[/tex]
Therefore, Slopes are Equal Hence the Lines are Parallel not Perpendicular.
For Perpendicular we require
[tex]m1\times m2=-1[/tex]
Therefore,
Slopes are Equal, Hence the Lines are not Perpendicular.
will reward brainliest!
how many and what type of solutions does the equation have 17+3x^2=6x
A. no real solution
B. one real solution
C. two rational solutions
D. two irrational solutions
Option D: Two irrational solutions
Explanation:
The equation is [tex]17+3 x^{2}=6 x[/tex]
Subtracting 6x from both sides, we have,
[tex]3x^{2} -6x+17=0[/tex]
Solving the equation using quadratic formula,
[tex]x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}[/tex]
Simplifying the expression, we get,
[tex]\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}[/tex]
Taking out the common terms and simplifying, we have,
[tex]\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}[/tex]
Dividing by 3, we get,
[tex]x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}[/tex]
Hence, the equation has two irrational solutions.
what is the product of r^2 -3 and 2r
Answer:
- 6r³.
Step-by-step explanation:
Here, we have to find the product of r², - 3 and 2r.
Now, the product is, P = (r²)(- 3)(2r)
⇒ [tex]P = (- 3) \times (2) \times r^{2}\times r[/tex]
{Seperating each terms as the terms are in product form}
⇒ [tex]P = - 6 \times r^{2 + 1}[/tex]
{Using the property of exponent that [tex]x^{a}\times x^{b} = x^{a + b}[/tex]}
⇒ P = - 6r³ (Answer)
write an algebraic expression for the following: the product of 5 and the sum of 9 and y. if y = 3 what’s the value of the expression
Answer:
60
Step-by-step explanation:
5 x (9 + y)
= 5 x ( 9 + 3)
= 5 x (12)
=60
Final answer:
The algebraic expression is 5(9 + y), which becomes 5(12) when y equals 3, resulting in a value of 60.
Explanation:
The algebraic expression for the product of 5 and the sum of 9 and y is 5(9 + y). To find the value of this expression when y equals 3, you substitute 3 for y in the expression, getting 5(9 + 3). Following the order of operations, calculate the sum inside the parentheses first, which gives you 5(12), and then multiply by 5 to find the product, resulting in a final value of 60.
Koby's solution for 4(x - 3) = x + 2 is shown at the
right. Did he solve the equation correctly? Explain why
or why not.
4(x - 3) = 3x +2
4x - 12 = 1/x + 2
2. (4X – 12) = 2 · ( 3x + 2
8x - 12 = x + 2
8x = x + 14
7x = 14
x
=2
Koby did not solve the equation correctly. The correct solution for 4(x - 3) = x + 2 is x = 14/3 or approximately 4.667. The steps include distribution, combining like terms, and isolating the variable.
The student's solution contains errors in the algebraic process. The correct steps to solve the original equation 4(x - 3) = x + 2 are as follows:
Distribute the 4 into the parentheses: 4x - 12 = x + 2.
Subtract x from both sides to get all the x terms on one side: 4x - x - 12 = 2.
Simplify the equation: 3x - 12 = 2.
Add 12 to both sides to isolate the variable term: 3x = 14.
Divide both sides by 3 to solve for x: x = 14/3.
The correct solution is x = 14/3 or approximately 4.667, not x = 2 as Koby had. To check the solution, you substitute the value back into the original equation:
4(14/3 - 3) = 14/3 + 2
which simplifies to:
56/3 - 12 = 14/3 + 2
and further to:
56/3 - 36/3 = 14/3 + 6/3
resulting in an identity:
20/3 = 20/3.
The diagram shows a sketch of John's yard. He wants to plant grass, so he must calculate the area of the yard. The distance from A to B is 200 feet; the distance from C to D is 260 feet, and the straight line distance between AB and DC is 220 feet. The area of the yard is
A) 5,720,000 square feet
B) 25,300 square feet
C) 50,600 square feet
D) 57,200 square feet
The area of the yard is 50,600 square feet.
Option: C.
Step-by-step explanation:
The given information forms a trapezoid.
The AB is the upper base (a) and its length is 200 feet.
The CD is the lower base (b) and its length is 260 feet.
A straight line distance from AB and CD is the height (h) and its measures as 220 feet.
The area of trapezoid A= [tex]\frac{a+b}{2} (h)[/tex].
A= [tex]\frac{200+260}{2} (220)[/tex].
=[tex]\frac{460}{2}(220)[/tex].
=230(220).
=50600 [tex]ft^2.[/tex]
Thus the area of John's yard is 50,600 square feet.
how do you solve a quadratic function using x^2+bx+c?
Answer:
Check the attachment, then plug in values as needed
Step-by-step explanation:
Layla is walking in a rectangular park. She walks one side that is 50 yards and then the other
side that is 120 yards. Layla develops a cramp in her leg and walks diagonally through the park
to head back home. What is the total distance that layla walked? (HINT: Final answer is
perimeter of the triangle park)
120 yd.
PARK
PARK
50 vd
Oak St
1
Park Rd
Total distance walked by Layla is 300 yards
Solution:
Given that,
Layla is walking in a rectangular park
She walks one side that is 50 yards and then the other side that is 120 yards
Length = 120 yards
Width = 50 yards
Layla develops a cramp in her leg and walks diagonally through the park to head back home
Let us find the length of diagonal of rectangle
[tex]d=\sqrt{w^2+l^2}[/tex]
[tex]d = \sqrt{50^2+120^2}\\\\d = \sqrt{2500+14400}\\\\d = \sqrt{16900}\\\\d = 130[/tex]
Thus length of diagonal is 130 yards
What is the total distance that layla walked?
Given that Final answer is perimeter of the triangle park
The diagonal and length and width forms a right angle triangle
Perimeter of triangle = diagonal length + width + length
Perimeter of triangle = 130 + 50 + 120 = 300
Thus total distance walked by Layla is 300 yards
The total distance Layla walked, including the two sides of the park and the diagonal path, is calculated using the Pythagorean theorem to be 300 yards.
Explanation:The question asks us to find the total distance Layla walked while going through the rectangular park diagonally. Layla first walks one side of the park which is 50 yards long and then the adjoining side which is 120 yards long. To do this, we will first find the length of the diagonal using the Pythagorean theorem and then add it to the sum of the two sides she walked to get the total distance. The Pythagorean theorem states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c2 = a2 + b2.
Applying the Pythagorean theorem to find the diagonal (hypotenuse):
Let a = 50 yards (length of the first side)Let b = 120 yards (length of the second side)c2 = a2 + b2 = 502 + 1202c2 = 2500 + 14400c2 = 16900c = √16900 = 130 yards (length of the diagonal)Now, we can find the total distance Layla walked:
Distance along the first side = 50 yardsDistance along the second side = 120 yardsDistance diagonally across the park = 130 yardsTotal distance = 50 yards + 120 yards + 130 yardsTotal distance = 300 yardsTherefore, the total distance Layla walked is 300 yards.
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Can anyone help me with theses problems?
What is the answer
9:3 :: 49 :
To solve this ratio problem, we need to determine the relationship between the given numbers and apply it to find the answer.
Explanation:The given expression is:
9:3 :: 49 :
To solve this, we need to determine the relationship between 9 and 3, and then apply the same relationship to 49.
The symbol '::' represents the ratio or proportion between the numbers before and after it.
9 divided by 3 is equal to 3, so the relationship here is that the first number is three times the second number.
Now, let's apply the same relationship to 49:
49 divided by 3 is equal to 16.33, so we can say that the answer is 16.33.
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The final answer is 9 : 3 :: 49 : 16.33.
Here's a step-by-step solution:
We need to find the missing number such that the ratios are equivalent. This can be written as a proportion: 9/3 = 49/x.First, simplify the left side: 9/3 = 3.So, we have: 3 = 49/x.Next, solve for x by multiplying both sides by x: 3x = 49.Finally, divide both sides by 3 to isolate x: x = 49/3.Therefore, x = 16.33 (rounded to two decimal places).The answer to the question is therefore 49 : 16.33.
Which statements are true about the area of a circle check all that apply
Answer:
The correct answer is Area = Pir2, The area formula can be found by breaking apart the circle and forming a parallelogram, and The area formula can be found by breaking apart the circle and forming a parallelogram. B,D,and E.
Step-by-step explanation:
Answer:
B, D, E
Step-by-step explanation:
Thats the correct answer bye
Melissa sells her art online for $49.50 per print. How many prints must she sell next month if she wants to earn at least $2000?
Answer:
41
Step-by-step explanation:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. 40 prints must she sell next month if she wants to earn at least $2000
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
Melissa sells her art online for $49.50 per print.
We need to find how many prints she has to sell to earn atleast $2000.
Let us consider x be the number of prints.
Let us form proportional equation
Forty nine point five zero by one equal tp two thousand by x.
49.50/1=2000/x
Apply cross multiplication
49.50x=2000
Forty nine point five zero times of x equal to two thousand.
Divide both sides by 49.50
x=40.40
Hence 40 prints must she sell next month if she wants to earn at least $2000
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Select the correct answer.
AB and BC form a right angle at point B. If A= (-3,-1) and B = (4,4), what is the equation of
O A.
x + 3y = 16
B. 2x + y = 12
C.-7x- 5y = -48
D. 7x - 5y = 48
Answer:
C. -7x- 5y = -48
Step-by-step explanation:
The vector AB is ...
AB = B -A = (4, 4) -(-3, -1) = (4+3, 4+1) = (7, 5)
The dot-product of this vector and the one in the direction of the line through B will be 0:
(7, 5)·(x -4, y -4) = 0
7(x -4) +5(y -4) = 0
7x +5y -48 = 0
Multiplying by -1 gives the form we see in answer choice C:
-7x -5y = -48
Write an equation for the nth term of the geometric sequences. Then Find a6
A. 2, 8, 32, 128, ...
B. 0.6, -3, 15, -75, ...
C. -1/8, -1/4, -1/2, -1, ...
D. 0.1, 0.9, 8.1, 72.9, ...
Answer: The nth term of a geometric progression is Tn = ar^(n-1)
A. 12
B. 3.6
C. -3/4
D. 0.6
Step-by-step explanation:
The nth term of a geometric progression is Tn = ar^(n-1)
Where Tn= nth term
a = first term
r = common ratio
n = number
A. a6 = (2*6) = 12
B. a6 = (0.6*6) = 3.6
C. a6 = (-1/8*6) = -3/4
D. a6 = (0.1*6) = 0.6
An angle with a measure of 36(degrees)would be classified as which type of angle?
Answer:
An acute Angle
Step-by-step explanation:
Any Angle that is from 1 to 89 degrees is considered an acute Angle.
The exterior angles of triangle UVW are ∠X, ∠Y, and ∠Z, and they are adjacent to ∠U, ∠V, and ∠W, respectively.
If m∠U is 33°, and m∠Z is 130°, what is m∠V?
Answer:
the answer is 97, I'll explain in the comments in a bit
^^
guy above me its right