Although the actual amount varies by season and time of day, the average volume of water that flows over the falls each second is 5.25.2 times ×10 Superscript 5105 gallons. How much water flows over the falls in an hour? Write the result in scientific notation. (Hint: 1 hour equals 3600 seconds)
The amount of water flowing each second is:
rate = 5.2 x 10^5 gallons / second
Since we know that:
1 hour = 3600 seconds
Therefore:
rate = (5.2 x 10^5 gallons / second) * (3600 seconds / hour)
rate = 1.872 x 10^9 gallons / hour
Final answer:
The average volume of water that flows over the falls in an hour is 1.89 x 10^9 gallons/hour.
Explanation:
To calculate the amount of water that flows over the falls in an hour, we need to convert the given flow rate from gallons per second to gallons per hour.
There are 3600 seconds in an hour, so we can multiply the flow rate (5.25 x 105 gallons per second) by 3600 to find the flow rate in gallons per hour.
The calculation would be: 5.25 x 105 gallons/s * 3600s/hour = 1.89 x 109 gallons/hour.
The result, in scientific notation, is 1.89 x 109 gallons/hour.
Given right triangle MNO, which represents the value of cos(M)?
a) ON/MN
b) MN/MO
c) ON/MO
d) MN/ON
The option that represents cos M is MN / MO
Using trigonometric ratios, we can find the ratio of sides of a right angle triangle.
Trigonometric ratios:sin x = opposite / hypotenusecos x = adjacent / hypotenusetan x = opposite / adjacentTherefore,
cos M = adjacent / hypotenuse
cos M = MN / 0M
Therefore, cos M = MN / MO
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Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.
(5, −12)
(−3, 0)
(−1, −1)
(0, 1)
(4, −12)
we will proceed to resolve each case to determine the solution
we have
[tex]2x+y>-4[/tex]
[tex]y>-2x-4[/tex]
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
case a) [tex](5,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*5-4[/tex]
[tex]-12>-14[/tex] ------> is True
therefore
the ordered pair [tex](5,-12)[/tex] is a solution of the inequality
case b) [tex](-3,0)[/tex]
Substitute the value of x and y in the inequality
[tex]0>-2*-3-4[/tex]
[tex]0>2[/tex] ------> is False
therefore
the ordered pair [tex](-3,0)[/tex] is not a solution of the inequality
case c) [tex](-1,-1)[/tex]
Substitute the value of x and y in the inequality
[tex]-1>-2*-1-4[/tex]
[tex]-1>-2[/tex] ------> is True
therefore
the ordered pair[tex](-1,-1)[/tex] is a solution of the inequality
case d) [tex](0,1)[/tex]
Substitute the value of x and y in the inequality
[tex]1>-2*0-4[/tex]
[tex]1>-4[/tex] ------> is True
therefore
the ordered pair [tex](0,1)[/tex] is a solution of the inequality
case e) [tex](4,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*4-4[/tex]
[tex]-12>-12[/tex] ------> is False
therefore
the ordered pair [tex](4,-12)[/tex] is not a solution of the inequality
Verify
using a graphing tool
see the attached figure
the solution is the shaded area above the line
The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality
Mr. Lewis sees a red light ahead and applies the brakes on his car. The car travels 300.5 feet before coming to a stop. For each foot the car travels during this time, its speed changes by −0.2 miles per hour.
What is the total change in the car's speed during that time?
a) -36.15
b) -60.1
c) 60.10
d) 36.15
multiply 300.5 feet by -0.2 mph
300.5 * -0.2 = -60.1 change
FOR 10 POINTS WILL MARK BRAINLIEST It costs $175 to rent a jet ski for 2 hours. It costs $300 to rent a jet ski for 2 hours. It costs 300$ to rent a jet ski for 4 hours. Write an equation that represents the cost y (in dollars) of renting a jet ski for x hours
The equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.
Explanation:The equation that represents the cost y (in dollars) of renting a jet ski for x hours can be found by analyzing the given information. Let's break it down step by step:
We are given that it costs $175 to rent a jet ski for 2 hours. This means the cost per hour is $175 / 2 = $87.50.We are also given that it costs $300 to rent a jet ski for 4 hours. This means the cost per hour is $300 / 4 = $75.Based on these two data points, we can see that as the number of hours increases, the cost per hour decreases. Therefore, we can infer that the cost of renting a jet ski is a linear function of the number of hours.Now, let's use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.Therefore, the equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.
The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward. Which statements are true? Check all that apply.
Answer:
A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.
C. The ball reaches its maximum height about 4 seconds after it is thrown
Step-by-step explanation: • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.
• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.
• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.
• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.
• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.
What is the greatest common factor of 120 60 160?
Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5).
A. 104
B. −246
C. 146
D. 250
Answer:
Option A is correct
The value of (h ∘ g)(−5) is, 104
Step-by-step explanation:
Given the functions:
g(x) = 2x
[tex]h(x) = x^2 + 4[/tex]
We have to find (h ∘ g)(−5).
[tex](h o g)(-5) = h(g(-5))[/tex] ....[1]
At x = -5
g(-5) = 2(-5) = -10
then
Substitute the g(-5) in [1] we have;
[tex](h o g)(-5) = h(-10)[/tex]
⇒[tex](h o g)(-5) = (-10)^2+4 = 100+4 = 104[/tex]
⇒[tex](h o g)(-5) = 104[/tex]
therefore, the value of (h ∘ g)(−5) is, 104
BRAINLIETS ND POINTSTO ANSWER THAT SHOWS ALL WORK YOU MIGHT NEED TO WORK OUT ON PAPER!!!
you are given the following equation:
+6=4/5(+3)
3a. Identify the slope of the equation.
3b. Identify the point used in the equation.
3c. Graph the equation.
E.j. found a $45 sweater on sale for $27. what is the percent of discount?
If you multiply a number by 3 and then subtract 5 you will get 40 what is the number
To find the answer the question first write it out. 3*x-5=40. move the five over next to the 40 and cancel out -5. so the new equation looks like this. Then add 40+5 which is 45.Lastly you have the number 3 and the variable x. now you have to divide 3 by 45 to get your final answer 15. so x=15.
3*x=40+5
3*x=45
Hope this helps!!
What is the median for this set of numbers?
10, 9, 23 , 68, 70, 4, 12, 4
Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work. 1/4X^3=-27/4
Answer:
x=3
Step-by-step explanation:
(c) what is the probability that diameter is within 2 mm of the mean diameter? (round your answer to three decimal places.)
a. Probability density function (pdf) of X: 0.247 for 0.20 < x < 4.25.
b. Probability that diameter exceeds 2 mm: 0.556.
c. Probability that diameter is within 2 mm of the mean diameter: 0.988.
(a) Probability density function (pdf) of X:
For a uniform distribution with A = 0.20 and B = 4.25, the pdf is constant within the range A to B and 0 elsewhere. Therefore:
f(x) = 1 / (B - A) = 1 / (4.25 - 0.20) = 1 / 4.05 ≈ 0.247 for 0.20 < x < 4.25
(b) Probability that diameter exceeds 2 mm:
P(X > 2) = (4.25 - 2) * f(x) = 2.25 * 0.247 ≈ 0.556
(c) Probability that diameter is within 2 mm of the mean diameter:
The mean of a uniform distribution is (A + B)/2 = (0.20 + 4.25)/2 = 2.225.
So, we need to find P(2.225 - 2 < X < 2.225 + 2), which is P(0.225 < X < 4.225).
P(0.225 < X < 4.225) = (4.225 - 0.225) * f(x) = 4 * 0.247 ≈ 0.988
Complete question:
An article considered the use of a uniform distribution with
A = 0.20 and B = 4.25
for the diameter X of a certain type of weld (mm).
(a) Determine the pdf of X. (Round your answers to three decimal places.)
0.2<x<4.25
(b) What is the probability that diameter exceeds 2 mm? (Round your answer to three decimal places.)
(c) What is the probability that diameter is within 2 mm of the mean diameter? (Round your answer to three decimal places.)
Your friend weights 62 kg, how many grams is this?
find the sum. 12x2 + 9x2=
To calculate the sum of 12x² + 9x², add the coefficients (12 and 9) to get 21 and then multiply by x², resulting in a sum of 21x².
To find the sum of the expression 12x² + 9x², you simply add the like terms. Both terms have an x² component, so they can be combined.
Here's how you do it:
First, identify the coefficients of the x² terms, which are 12 and 9.
Next, add these two coefficients together: 12 + 9 = 21.
Finally, multiply the sum of the coefficients by x2 to get the final answer: 21x².
Therefore, the sum of 12x² + 9x² is 21x².
Solve by quadratic formula
Solve for x. 9(x - 2) = 18
x = 0
x = 16/9
x = 20/9
x = 4
Explain how to multiply the complex #'s (3+2i)(4-i)
Perry surveyed 60 students at her school and found that 0.45 of the students she surveyed said their favorite class is math. Another 35% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science? 6 7 27 21
Factor 64-x^15 in mathhhhgg
Answer:
Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Step-by-step explanation:
We need to factor the expression [tex]64-x^{15}[/tex]
Re-write the given expression [tex]64-x^{15}[/tex] as;
[tex]4^{3}-(x^{5})^{3}[/tex]
Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]
so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]
[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Hence, factor of [tex]64-x^{15}[/tex] is
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
The value of factor of expression 64 - x¹⁵ is,
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
We have to given that;
To factor the expression,
⇒ 64 - x¹⁵
Now, We can simplify as;
⇒ 64 - x¹⁵
⇒ 4³ - (x⁵)³
⇒ (4 - x⁵) (4² + 4x⁵ + (x⁵)²)
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
Therefore, The value of factor of expression 64 - x¹⁵ is,
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
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Will Give BRAINLIEST) the distance around a rectangular parking lot is 1,200 meters. If the parking lot is 74 meters long, how wide is it?
Hank draws a line with a zero slope through the points (–2, 4) and (3, b). Which value of b could represent Hank’s second point? –3 –1 4 9
As per the slope of a line, the value of 'b' is 4.
What is the slope of a line passing through two points?The slope of a line(m) passing through two points (x₁, y₁) and (x₂, y₂)can be represented as:
m = (y₂ - y₁)/(x₂ - x₁)
Given, the slope of the line is (m) = 0.
Here the given points are (–2, 4) and (3, b).
Therefore, substituting the values, we get:
0 = (b - 4)/[(3 - (- 2)]
⇒ (b - 4)/5 = 0
⇒ b - 4 = 0
⇒ b = 4
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Sam and chad are ticket-sellers at their class play. sam is selling student tickets for $2.00 each, and chad selling adult tickets for $5.50 each. if their total income for 24 tickets was $83.00, how many tickets did sam sell?
The number of tickets sold to students by Sam will be 14.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sam and Chad are ticket-sellers at their class play. Sam is selling student tickets for $2.00 each, and Chad selling adult tickets for $5.50 each. if their total income for 24 tickets was $83.00.
Let x be the number of tickets sold to students and y be the number of tickets sold to adults. Then the equation is given as,
x + y = 24 ...1
2x + 5.5y = 83 ...2
From equations 1 and 2, then we have
2(24 - y) + 5.5y = 83
48 - 2y + 5.5y = 83
3.5y = 35
y = 10
Then the value of x will be given as,
x + 10 = 24
x = 24 - 10
x = 14
The number of tickets sold to students by Sam will be 14.
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A bottle of soft drink is two thirds full. Jack drinks one quarter of the remaining soft drink. How full is the bottle now
Charli,
First find what 1/4 of 2/3 is.
1/4 of 2/3 = 1/6
(That is 1/4 times 2/3 = 1/6)
So, the bottle was 2/3 full, it is now ...
2/3 - 1/6
=4/6 - 1/6
= 3/6 or 1/2 full.
We know that the bottle of soft drink has a remaining volume which is 2 / 3 of the original.
Since Jack drank 1 / 4 of the remaining volume, hence only 3 / 4 now finally remains, the total is:
(2 / 3) * (3 / 4) = 6 / 12 = 1 / 2
Hence the bottle is now one half full
Point M is the midpoint of AB . AM= 3x+3, and AB=8x−6
What is the length of AM?
The answer is 21 but i don't know the steps to get it. HELP
The length of AM is:
21 units.
Step-by-step explanation:Point M is the midpoint of AB.
AM= 3x+3, and AB=8x−6
Since, the midpoint divides the line segment into two equal parts i.e. it bisects the line segment.
Hence, we have:
AM+MB=AB
Also, AM=MB
Hence, we have:
[tex]3x+3+3x+3=8x-6[/tex]
on combining the like terms in the left hand side of the equation we have:
[tex]3x+3x+3+3=8x-6\\\\6x+6=8x-6[/tex]
Now, on subtracting both side of the equation by 6x we have:
[tex]6=8x-6-6x\\\\6=8x-6x-6\\\\6=2x-6[/tex]
on adding 6 on both side of the equation we have:
[tex]6+6=2x\\\\12=2x\\\\2x=12\\\\x=\dfrac{12}{2}\\\\x=6[/tex]
Hence, we have:
[tex]AM=3\times 6+3\\\\AM=21\ \text{units}[/tex]
Bens date of birth is a prime number between 15 and 25. This number has 57 as a multiple.
What is the conclusion of the following conditional a number is divisible by two if the number is even
Yearly attendance at a local movie theater is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theater in nine years?
The approximate attendance at the movie theater in nine years, with a continuous growth rate of 4.2%, is around 79,918.
Explanation:The question provided can be solved using the formula for continuous growth, A = P ert, where A is the final amount, P is the initial principal amount (56,000 in this case), r is the rate of growth (4.2% or 0.042 when expressed as a decimal), and t is time in years (9 years here).
To find the approximate attendance at the movie theater in nine years, we substitute our values into the formula: A = 56000 x e(0.042 x 9). After calculating this, we find that the approximate attendance at the movie theater after nine years is about 79,918.
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Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options:
Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months.
Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement?
a. Only option A will allow them to meet their goal.
b. Only option B will allow them to meet their goal.
c. Both options A and B will allow them to meet their goal.
d. Neither option A nor option B will allow them to meet their goal.
Answer: D (Neither option A nor option B will allow them to meet their goal.
Hope this helps!