On March 24, 1989, the Exxon Valdez oil tanker ran aground and leaked millions of gallons of oil into Prince William Sound. The spill covered approximately 11,000 square miles of ocean. The oil spread out in a circular pattern and the radius increased by 0.10 mph. Use π = 3.14. At this rate, how many hours did it take for oil to cover the area?
Answer:
592 hours
Step-by-step explanation:
Given
[tex]Area = 11000m^2[/tex]
[tex]Radius = 0.10m/h[/tex]
Required
Determine the time taken to cover the area
Since, the oil formed a circular pattern; the question will be answered using area of a circle
[tex]Area = \pi r^2[/tex]
Let t represent the time take to cover 11000m²;
The relationship between these parameters is:
[tex]11000 = \pi * (0.10t)^2[/tex]
Substitute 3.14 for π
[tex]11000 = 3.14 * (0.10t)^2[/tex]
Divide both sides by 3.14
[tex]\frac{11000}{3.14} = \frac{3.14 * (0.10t)^2}{3.14}[/tex]
[tex]\frac{11000}{3.14} =(0.10t)^2[/tex]
[tex]3503.18471338 = (0.10t)^2[/tex]
Take square root of both sides
[tex]\sqrt{3503.18471338} = \sqrt{(0.10t)^2}[/tex]
[tex]\sqrt{3503.18471338} = 0.10t[/tex]
[tex]59.1877074516 = 0.10t[/tex]
Divide both sides by 0.10
[tex]\frac{59.1877074516}{0.10} = \frac{0.10t}{0.10}[/tex]
[tex]\frac{59.1877074516}{0.10} = t[/tex]
[tex]591.877074516 = t[/tex]
[tex]t = 591.877074516[/tex]
[tex]t = 592\ hours[/tex] (Approximated)
Hence, it'll take approximately 592 hours to cover the given area
Answer: B
592 hours
Step-by-step explanation:
We started with five gallons of an orange drink that was 90% water and 10% syrup. We added 1 gallon of concentrate and ended up with a resulting mixture that was 86% water and 14% syrup. Determine what percent of the concentrate was water and what percent was syrup.
Answer:
The gallon of concentrate was 66% water and 34% syrup.
Step-by-step explanation:
- The first thing is to know how much water and how much syrup have the 5 gallons.
90% water and 10% syrup.
- If we have 5 gallons with the same percentages then:
Where X is the percentage that we do not know.
(90 + 90 + 90+ 90 + 90 + X) / 6 = 86
(90 + 90 + 90+ 90 + 90 + X) = 516
X = 66
The answer is 66% water in the gallon added.
56 points! Please help
Answer:
Segment bisector: JK
MN= 52
Step-by-step explanation:
The segment bisector basically means the point where the line is cut in half. If you study the figure, you can see the two small red lines intersecting The longer line. This means that the two small black segments are equal to each other. With this in mind, we now know that the segment bisector is line JK.
To find the length of MN, study the figure again. You can see that we are given the value of one line segment that is half the length of MN. So all we need to do is multiply that value by 2:
[tex]26*2=52[/tex]
The length of line segment MN is 52.
:Done
Answer:
MN = 52
Step-by-step explanation:
bisector is just a half of its length
looking through the graph
MN = 26 * 2 (just multiply ot by 2)
MN = 52
The edge length of a cube with volume 24 cubic units
Answer:
2∛3 units
Step-by-step explanation:
The volume is the cube of the edge length, so the edge length is the cube root of the volume:
s = ∛V
s = ∛24 = ∛(2³·3)
s = 2∛3
The edge length is 2∛3 ≈ 2.8845 units.
John left his house in Irvine at 8:20 AM to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50 AM. At 5:30 PM, he left the meeting and drove home. He arrived home at 7:45 PM.
What integer is closest to −7π?
Answer:
[tex]\Huge \boxed{-22}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]-7\pi[/tex]
We can take pi as 22/7.
[tex]\Longrightarrow \displaystyle \ \ -7 \times \frac{22}{7}[/tex]
[tex]\Longrightarrow \displaystyle \ \ 22 \times \frac{7}{-7}[/tex]
[tex]\Longrightarrow \displaystyle \ \ 22 \times -1[/tex]
[tex]\Longrightarrow \displaystyle \ \ -22[/tex]
[tex]\rule[225]{225}{2}[/tex]
The integer closet to -7π is -22.
What is integer?An integer is a number that includes both negative and positive numbers, including zero, and does not have a decimal or fractional component. Examples of integers include: -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that includes the following:
Positive figures: If a number is greater than zero, it is positive. Example: 1, 2, 3 . . .
Negative Counts: If a number is less than zero, it is negative. Example: -1, -2, -3 . . .
Zero cannot be thought of as either a negative or a positive number. It's a complete number.
Given -7π
the value of π in fraction form is 22/7
substitute the value of π
-7π = -7 x 22/7
-7π = -22
Hence, -22 is integer is closest to −7π.
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3. What is the Kinetic Energy of a 100 kg object that is moving with a speed of 12.5 m/s?
Answer:
7812.5 J
Step-by-step explanation:
Kinetic energy is equal to 1/2 m v^2.
The mass of the object is 100 and the velocity is 12.5 m/s.
Therefore, the kinetic energy is 1/2 (100) (12.5)^2 = 7812.5 J.
Answer:
KE = ½ (100kg) (12.5 m/s)2
KE = ½ (100kg)(156.25)
KE = 7,812.5J
answer ^
Step-by-step explanation:
KE = ½ mv2
KE = ?
m = 100kg
v = 12.5m/s
Can someone help??????
Answer:
$159.5
Step-by-step explanation:
the price should be increased by 5%.
which means the old price would be 95% of the new price.
168×95=15960
15960÷100=159.6
The volume, in cubic feet, of a right cylindrical silo of height and radius is [tex]V = \pi r^2h[/tex] The height of the silo is h(r) = 3.5r. Which statements are true regarding the functions described?
A. To get a volume of 100 cubic feet, the radius must be 2 feet.
B. The domain of [tex]V(h(r))[/tex] is restricted to values of r greater than 0.
C. The output of V is the input of h
D. [tex]V(h(r)) = 3.5\pi r^3[/tex]
E. The volume depends on the radius of the cylinder
1. The domain of [tex]V (h(r))[/tex] is restricted to values of r greater than 0.
2. [tex]V(h(r)) = 3.5\pi r^3[/tex]
3. The volume depends on the radius of the cylinder
What is this answer please help someone
Answer:
I think the answer is line DE
Choose all sets that contain the number –2.22.
Answer:
it is only the RATIONAL numbers who can contain that number
Answer:
rational and real numbers!!
Step-by-step explanation:
if point C is between points A and B, then AC+CB=______?
Answer:
AB
Step-by-step explanation:
A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be
Answer:
H0 : u = 45
H : u not equal to 45
This is because the topic of claim or contention is that the average minutes a student need to complete the statistics exam is 45mins
A magician flips a coin 8 times producing heads each time. Is there statistical significance to say that the coin is somehow rigged?
A. Yes, because the results are unlikely to happen by chance.
B. No, because the results are unlikely to happen by chance.
C. Yes, because the results are likely to happen by chance.
D. No, because the results are likely to happen by chance.
Answer:
A
Step-by-step explanation:
Either a or b could work, but he's a magician so it's probably rigged
Solve the problem
X/5 +4=17
Answer:
x = 65
Step-by-step explanation:
X/5 +4=17
Subtract 4 from each side
X/5 +4-4=17-4
x/5 = 13
Multiply each side by
x/5 *5 = 13*5
x = 65
Answer:
x=65
Step-by-step explanation:
x/5+4=17
solve for x by simplifying for both sides of the equation, then isolate the variable. x=65
Jo is 5 cm taller than Kathy.Let k=kathy height.Then? = Jo height
Answer:
5+k
Step-by-step explanation:
Since k is Kathy's height and we know Jo is 5+ cm than Kathy. That makes Jo = 5+k
It’s going in a pattern I’m not doing it
Answer:
They keep adding 3x as much
Round 8,503 to nearest thousand
Answer:
9,000
Step-by-step explanation:
If x < 5, we round down.
If x ≥ 5, we round up.
Since 8,503, 500 is ≥ 5, we round up to 9. So,
8,503 ≈ 9,000
Answer:
9,000
Step-by-step explanation:
Look to the hundreds place. If the number is 4 or below we round down. If the number is 5 or above we round up.The number is 5, so we round up. The 8 in the thousands place becomes a 9, and the other places become 0s. Write out the newly rounded number: 9,000You're done! I hope this helps!
is square root of 140 a rational or irrational number ?
Answer: The square root of 140 is irrational.
Step-by-step explanation:
Take the square root of 140:
11.8321595662
This is an imperfect square root, and all imperfect square roots are irrational.
"-8 is 12 less than a number."
Answer:
The answer would be x<4
Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. slope = -5, passing through (4,-2)
Answer:
Step-by-step explanation:
y + 2 = -5(x - 4)
y + 2 = -5x + 20
y = -5x + 18
Solve the equation x+2/3=18
Answer: x=52/3
Step-by-step explanation:
x+2/3=18
x=18-2/3 ⇔ subtraction property of equality
x=54/3-2/3 ⇔ convert integer into fraction
x=52/3
Hope this helps!! :)
Answer:
see below
Step-by-step explanation:
( x+2)/3=18
Multiply each side by 3
(x+2)/3 *3 = 18*3
x+2 = 54
Subtract 2
x+2-2 =54-2
x = 52
or if
x+2/3=18
Subtract 2/3
x+2/3 -2/3 = 18-2/3
x = 17 +1 -2/3
x = 17 1/3
What is the solution to this system of equations using the linear combination method?
4x + y = 5
3x + y = 8
(0, – 3)
(-3, 17)
(0,5)
(2, -3)
Answer:
My answer is (-3, 17).
Step-by-step explanation:
You will use minus sign for the equation in other to eliminate one of the letters and use the other one to find the one eliminated later...Which means that 4x+y=5 (-) 3x+y=8..... the minus sign will eliminate +y and +y in each equation because the "+y" in the second equation will be turned to -y because + times(×) - will give us minus sign so the "y" will be eliminated to give space for the 'x" .After the x has been found which is x=-3 then you will substitute x=-3 into the any equation and then you will also find the "y" which is y=17.....Thank you
If point X is between W and Y then WX + XY = WY.
always
sometimes
never
Answer:
Always
Step-by-step explanation:
lets say WY = 8
WX = 2
hope this helps
XY = 6
WX(2) + XY(6) = 8
Answer:
always
Step-by-step explanation:
The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The critical value for a 95% confidence interval around this sample mean is ________.
Answer:
2.06
Step-by-step explanation:
The formula for critical value = Margin of Error / Standard Error
Margin of Error = z × Standard deviation/√n
Mean for the month of March = $305.30
Standard deviation = $46.50
n = number of samples = 26 homes
z score for 95% confidence interval = 1.96
= 1.96 × $46.50/√26
= 17.874024556
Standard error = standard deviation/√n
= $46.50/√26
= 9.1194002839
Critical value = Margin of Error/Standard Error
= 17.874024556/9.1194002839
= 2.06
What is the product of the polynomials below?
(7x2+2x+4)(2x+5)
Answer:
This is a simple multiplication problem.
Here is my steps:
(14x^3 + 35x^2 + 4x + 10x + 8x + 20)
Combine like terms:
(14x^3 + 35x^2 + 22x + 20)
And that is your answer^^
Answer:
14x3+ 39x2 +8x +20
Step-by-step explanation:
Use the distributive property and/or the FOIL (front, outer, inner, last) method.
First:
Multiply (7x2)(2x)
=14x3
Then (7x) (5)
=35x2
Second:
Multiply (2x)(2x)
=4x2
Then (2x)(5)
=10
Third:
Multiply 4(2x)
=8x
Then (4)(5)
=20
You should get:
14x3 +35x2 +4x2 +10 +8x +10
Add all common numbers.
You should get:
14x3+ 39x2 +8x +20
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why. f(x)=1050
Answer:
D
Step-by-step explanation:
The function f(x) = 1050 is a polynomial with degree zero option (A) this is a polynomial function of degree zero with a leading coefficient of 1,050 is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
The question is incomplete.
The complete question is:
Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a
polynomial, state why.
F(x) = 1,050
A. This is a polynomial function of degree zero with a leading coefficient of 1,050.B. This is not a polynomial. Horizontal lines can not be polynomials as there are no turning points.C. This is not a polynomial. Only vertical lines of the form x = b can be classified as a polynomial.D. This is not a polynomial because there are no variables.We have a function:
f(x) = 1050
We can write it as:
f(x) = 1050x⁰
x⁰ = 1
As we know from the definition of the polynomial:
The polynomial is a combination of the variable and constant with powers of x that are non-negative.
f(x) = 1050 is a polynomial function of degree zero with a leading coefficient of 1,050.
Thus, the function f(x) = 1050 is a polynomial with degree zero option (A) this is a polynomial function of degree zero with a leading coefficient of 1,050 is correct.
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Which expressions are equal to 0 when x = -1? Check all that apply.
4(x + 1) divided by
(4x + 5)
4(x - 1) divided by
(5 - 4x)
4(x - (-1) divided by
(4x + 5)
04.(X + (-1) divided by
(4x + 5)
0 4(x + 1) divided by
(5 - 4x)
Answer:
A C and E
Step-by-step explanation:
how the number e was discover
Answer:
It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients
Find a linear inequality with the following solution set. Each grid line represents one unit. [asy] size(200); fill((-5,-3)--(5,2)--(5,5)--(-5,5)--cycle,yellow); real ticklen=3; real tickspace=2; real ticklength=0.1cm; real axisarrowsize=0.14cm; pen axispen=black+1.3bp; real vectorarrowsize=0.2cm; real tickdown=-0.5; real tickdownlength=-0.15inch; real tickdownbase=0.3; real wholetickdown=tickdown; void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { import graph; real i; if(complexplane) { label("$\textnormal{Re}$",(xright,0),SE); label("$\textnormal{Im}$",(0,ytop),NW); } else { label("$x$",(xright+0.4,-0.5)); label("$y$",(-0.5,ytop+0.2)); } ylimits(ybottom,ytop); xlimits( xleft, xright); real[] TicksArrx,TicksArry; for(i=xleft+xstep; i 0.1) { TicksArrx.push(i); } } for(i=ybottom+ystep; i 0.1) { TicksArry.push(i); } } if(usegrid) { xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true); yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows); } if(useticks) { xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); } else { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize)); } }; draw((-5,-3)--(5,2),dashed+red, Arrows(size=axisarrowsize)); rr_cartesian_axes(-5,5,-5,5); for( int i = -4; i 0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)
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