Answer:
It'll take a bucket loads of [tex]7 * 10^{20}[/tex] to empty world's ocean
Step-by-step explanation:
Given
[tex]World\ Ocean: 1.4 * 10^9 km^3[/tex]
[tex]Bucket: 20,000 cm^3[/tex]
[tex]1 km^3 = 10^{15} cm^3[/tex]
To get the number of bucket loads, we simply divide the size of the ocean by the size of the bucket;
[tex]Number = \frac{Ocean\ Size}{Bucket\ Size}[/tex]
[tex]Number = \frac{1.4 * 10^9 km^3}{20,000cm^3}[/tex]
Expand the numerator
[tex]Number = \frac{1.4 * 10^9 * 1km^3}{20,000cm^3}[/tex]
Recall that [tex]1 km^3 = 10^{15} cm^3[/tex]
So, the expression becomes
[tex]Number = \frac{1.4 * 10^9 * 10^{15} cm^3}{20,000cm^3}[/tex]
Simplify the numerator using laws of indices
[tex]Number = \frac{1.4 * 10^{9+15} cm^3}{20,000cm^3}[/tex]
[tex]Number = \frac{1.4 * 10^{25} cm^3}{20,000cm^3}[/tex]
Expand the denominator
[tex]Number = \frac{1.4 * 10^{25} cm^3}{2 * 10,000cm^3}[/tex]
[tex]Number = \frac{1.4 * 10^{25} cm^3}{2 * 10^4\ cm^3}[/tex]
Split fraction
[tex]Number = \frac{1.4}{2} * \frac{10^{25} cm^3}{10^4\ cm^3}[/tex]
[tex]Number = 0.7 * \frac{10^{25}}{10^4\ }[/tex]
Simplify fraction using laws of indices
[tex]Number = 0.7 * 10^{25-4}[/tex]
[tex]Number = 0.7 * 10^{21}[/tex]
[tex]Number = 7 * 10^{20}[/tex]
Hence, it'll take a bucket loads of [tex]7 * 10^{20}[/tex] to empty world's ocean
A train leaves Miami at 3:00 PM. A second train leaves the same city in the same direction at 8:00 PM. The second train travels 145 mph faster than the first. Of the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains
Answer:
The first train travels at 58 mph and the second train travels at 203 mph.
Step-by-step explanation:
The first train left Miami at 3:00 PM.
The second train left Miami at 8:00 PM.
Let the speed of the first train be x.
The second train travels 145 mph faster than the first, that is 145 + x
The second train overtakes the first at 10:00 PM
This means that at 10:00 PM, they were both at the same location.
That is 7 hours after the first train left and 2 hours after the second train left.
Speed is given as:
s = d / t
where d = distance traveled and t = time taken
For the first train, after 7 hours traveling at speed x:
x = d / 7
=> d = 7x _______(1)
For the second train, after 2 hours, traveling at speed 145 + x:
145 + x= d / 2
=> d = 290 + 2x ____(2)
Equating (1) and (2):
7x = 290 + 2x
=> 7x - 2x = 290
5x = 290
=> x = 290/5 = 58 mph
Therefore, the first train travels at 58 mph and the second train travels at 203 mph (58 + 145)
What is sixty dollars increased by fifteen percent?
Answer:
$69 dollars.
Step-by-step explanation:
$60 dollars increased by 15% is the same as:
60 + 60(.15) = 60(1.15) = $69
Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the standard normal table to find the following probabilities. Enter the probabilities as decimals. Enter the final answer only.
1.P(z>1.38)=
2.P(1.233.P(z<−0.42)=
3.P(z<−0.42)=
4. P(−2.645.P(z<3.04)=
5. P(z<3.04)
6.P(07.P(z>−2.43)=
7.P(z>−2.43)=
Answer:
(1) P (z > 1.38) = 0.08379
(2) P (z < - 0.42) = 0.33724
(3) P (z < 3.04) = 0.99882
(4) P (z > -2.43) = 0.00755
Step-by-step explanation:
(1)
Compute the value of P (z > 1.38) as follows:
[tex]P(z>1.38)=1-P(z<1.38)\\=1-0.91621\\=0.08379[/tex]
(2)
Compute the value of P (z < -0.42) as follows:
[tex]P(z<-0.42)=1-P(z<0.42)\\=1-0.66276\\=0.33724[/tex]
(3)
Compute the value of P (z < 3.04) as follows:
[tex]P(z<3.04)=0.99882[/tex]
(4)
Compute the value of P (z > -2.43) as follows:
[tex]P(z>-2.43)=1-P(z<2.43)\\=1-0.99245\\=0.00755[/tex]
The water usage at a car wash is modeled by the equation W(x) = 4x3 + 6x2 − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.
Write a function, C(x), to model the water used by the car wash on a shorter day
Answer:
The second option.
Step-by-step explanation:
We are trying to find what is W(x) - D(x).
(4x^3 + 6x^2 - 11x + 7) - (x^3 + 2x^2 + 15)
= 4x^3 - x^3 + 6x^2 - 2x^2 - 11x + 7 - 15
= 3x^3 + 4x^2 - 11x - 8
This corresponds to the second option.
Hope this helps!
A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
What is an equation?
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
The water usage at a car wash is modelled by the equation W(x) = 4x³ + 6x² − 11x + 7, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The amount of decrease in water used is modelled by D(x) = x³+ 2x² + 15, where D is the amount of water in cubic feet and x is time in hours.Now the amount of water is cut from the total water usage so to find out the new model c(x) we need to subtract the decrease in water from the total water usage.
We are trying to find what
C(x) = W(x) - D(x)
C(x) = ( 4x³ + 6x² − 11x + 7, ) - ( x³ + 2x² + 15 )
C(x) = 4x³ - x² + 6x² - 2x³ - 11x + 7 - 15
C(x) = 3x³ + 4x² - 11x - 8
Therefore A function, C(x), to model the water used by the car wash on a shorter day will be 3x³ + 4x² - 11x - 8
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how many stakes 5.5 feets long can be cut from 10 lengths of lumber each 12 feet long
Answer:
20 or 21 stakes
Step-by-step explanation:
It would be 20 if you were not able to use the extra wood after cutting two 5.5 foot long segments from each lumber. If you can use the extra 1 foot from each lumber then you would have an extra 10 feet of lumber which you could get one 5.5 foot long stake from.
The number of stakes will be 22.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that 5.5 feet long can be cut from 10 lengths of lumber each 12 feet long.
The total length is calculated as:-
Total length = 12 x 10 = 120 feet
Number of stakes = 120 / 5.5 = 21.81 ≅ 22
Hence, the number of stakes is 22.
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Which figure shows a line of reflectional symmetry for the letter T? A letter T is folded at the horizontal line. A letter T is folded diagonally. A letter T is folded vertically through the middle. A letter T is folded diagonally through its center.
Answer:
A letter T is folded vertically through the middle.
Step-by-step explanation:
Reflectional symmetry refers to the symmetry of line that divides the given shape into two equal halves. The halves represent the mirror reflection of each other. The line of symmetry is drawn to show the reflection and it acts as a mirror. For the letter 'T', the reflectional symmetry will be drawn vertically in the middle of the letter. The line divides the letter into two equal halves with mirror images.
The figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
What is a Line of Reflectional Symmetry?A line of reflectional symmetry can be described as an imaginary line that divides a figure into two halves in such a way that each of the halves are a mirror image of the other.
When a line divides letter T vertically, two mirror images are created.
Thus, the figure that will depict a line of reflectional symmetry of letter T would be: A letter T folded vertically through the middle.
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If f(x)=8-10x and g(x)=5x+4, what is he value of (fg)(-2)
Answer:
168
Step-by-step explanation:
We would like to multiply these two expressions together and then substitute -2 in for x to solve.
f(x) * g(x) = (8 - 10x) * (5x + 4)
We will use FOIL (first, outer, inner last):
(8 - 10x) * (5x + 4) = 8 * 5x + 8 * 4 + (-10x) * 5x + (-10x) * 4
Combining terms, we get:
f(x) * g(x) = 32 - 50x²
Plug -2 in for x:
32 - 50 * (-2)² = 32 - 50 * 4 = 32 - 200 = -168
The answer is thus 168.
~ an aesthetics lover
Gabriela has dinner at a cafe and the cost of her meal is
$
45.00
$45.00dollar sign, 45, point, 00. Because of the service, she wants to leave a
15
%
15%15, percent tip.
What is her total bill including tip?
Answer: 51.75
Step-by-step explanation: 15 precent of 45 is 6.75
Then add 45+6.75
Answer:
Her total including the bill will be $51.75
Step-by-step explanation:
15% of $45
= $6.75
$45 + $6.75 = $51.75
Henry wants to double a cake recipe that uses 2 cups and 10 tbsp of flour. How much flour will he need?
9514 1404 393
Answer:
5 cups and 4 tbsp
Step-by-step explanation:
Double the quantity (2 c, 10 T) is ...
2 × (2 c, 10 T) = (4 c, 20 T)
A cup is equal to 16 tablespoons, so this quantity can be rewritten as ...
(5 c, 4 T)
Five cups and four tablespoons of flour are needed for the double recipe.
Answer this ASAP please
A. a=2, b=27, c=3
B. a=2, b=-27, c=-3
C. a=2, b=-3, c=-27
D. a=2, b=3, c=27
Answer:
Third Choice: a = 2, b = -3, c = -27
Step-by-step explanation:
The equation to be solved with the quadratic formula must be written in the form
ax^2 + bx + c = 0
2x^2 = 27 + 3x
Subtract 3x from both sides. Subtract 27 from both sides.
2x^2 - 3x - 27 = 0
Now we see we have
a = 2, b = -3, c = -27
Answer: Third Choice
Match each polynomial expression to its additive inverse.
6x²-x-2
6x2 - x+2
6x2 - x+2
6x2 + x + 2
6x²+x-2
6x2 + x-2
6x2+x-2
-6,2-x+2
Answer:
Step-by-step explanation:
To find the additive inverse of polynomial expression, flip the sign of each term.
6x² ----> -6x²
-x -----> +x
-2 -----> +2
Additive inverse:
-6x² + x + 2
If i make $8.00 per hour and work 6 hours a day 5 days per week how much would my check be bi-weekly?
Answer:
480$
Step-by-step explanation:
Bi-weekly means every other week. So it is 6 times 5, because u work 30 hours a week. Than 30 (hours) times 8 (money per hour). This is 240 a week. So 240 times 2 is 480.
In the triangles, HG = MP and GK = PN. Triangles H G K and M P N are shown. Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters. Sides H G and M P are congruent. Sides G K and P N are congruent. Which statement about the sides and angles is true?
Answer:
m∠G > m∠P
Step-by-step explanation:
Given that:
HG = MP and GK = PN., Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters.
The triangle law for unequal sides states that if two sides are unequal. the angle opposite the longer side is greater than the angle opposite the shorter side. Since side HK has a length of 15 millimeters and Side MN has a length of 11 millimeters, the angle opposite side HK (which is m∠G) is greater than the angle opposite side MN (which is m∠P). That is m∠G > m∠P.
Answer:
A.
Step-by-step explanation:
s the ordered pair (6, 5) a solution to the equation 3x − 4y = −2?
Answer:
Yesh.
Step-by-step explanation:
3x - 4y = -2
3 * 6 - 4 * 5 = -2
18 - 20 = -2
-2 = -2
So, the ordered pair is a solution to the equation.
Hope this helps!
Answer:
Yes, it is
Step-by-step explanation:
If you add in the numbers, you get
(3*6)- (4*5)=-2.
then solving it, you get
18-20= -2
which is correct. (18-20 IS -2)
so, the ordered pair is a solution to the problem. Hope this helps :)
Find the distance between the points (4, 0) and (–3, 4).
Answer:
[tex]\huge\boxed{\sqrt{65}\approx8.062}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have two points (4, 0) and (-3, 4).
Substitute:
[tex]d=\sqrt{(-3-4)^2+(4-0)^2}=\sqrt{(-7)^2+4^2}=\sqrt{49+16}=\sqrt{65}[/tex]
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
f(x)=2(x-3)^2
Step-by-step explanation:
vertex form: a(x-h)^2+k
so find the vertex (h,k) and use it to turn it into vertex form
EXTRA POINTS! Evaluate the expression 7x2y, when x = 3 and y = 4. A.168 B.252 C.336 D.794
Answer:
A
Step-by-step explanation:
Put the values of x and y into the expression, then multiply the values.
7 x 3 x 2 x 4 = 168
Answer:
B. 252
Step-by-step explanation:
[tex]7x^2y[/tex]
Put x as 3 and y as 4.
[tex]7\left(3\right)^2\left(4\right)[/tex]
Evaluate.
[tex]7(9)(4)[/tex]
[tex]=252[/tex]
The origin is at (1, 1): that is, the origin is at position 1 on the x-axis and at position 1 on the y-axis.
Answer: What is the question? If you could be more specific I could try to help but there is no question here.
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
just did it
The product of a number and its inverse is 1. Represent it in algebraic form.
Answer:
Step-by-step explanation:
Hello
first of all we assume that this number is different from 0 as dividing by 0 is not allowed
let's not n this number
its inverse is
[tex]\dfrac{1}{n}[/tex]
and we can write
[tex]n*\dfrac{1}{n}=1[/tex]
hope this helps
Answer:
x * 1/x = 1
Step-by-step explanation:
Let x be the number
1/x is the inverse
x * 1/x = 1
Identify the fallacies of relevance, weak induction, presumption, ambiguity, and illicit transference committed by the following arguments, giving a brief explanation for your answer. If no fallacy is committed, write "no fallacy." When I visited Dr. Ames about my cholesterol, she insisted that I go on a statin drug. She says everybody should be on a statin. And when I saw Dr. Collins for depression, he prescribed Prozac. And when the Prozac gave me nausea, he prescribed Zofran to stop the nausea. Doctors are all the same. They all take their orders from the pharmaceutical industry.
Answer:
Hasty generalization fallacy
Step-by-step explanation:
Fallacy can be said to be a reasoning which leads to the wrong interpretation of a statement or an argument. Although some people intentionally make fallacious statements just to score cheap points or to please the listening audience, but some make fallacious unknowingly, either due to carelessness or by being lackadaisical.
In this case the writer, without enough investigation and proof, comes to a very hasty conclusion that "all doctors are the same". This is termed a hasty conclusion because the writer only had dealings with just two docotors(Dr. Ames and Dr. Collins). So saying all doctors are the same just because of two instance is a rather rash statement.
Therefore, the fallacy commited by the writer here is a fallacy of hasty generalization.
Hasty generalization fallacy occurs when someone has a limited information on a population but makes a conclusion based on a larger population than he/she should.
Simplest form w^3-w(w^2+2w-1)+2w
Answer:
[tex] - 2 {w}^{2} + 3w[/tex]Solution,
[tex] {w}^{3} - w( {w}^{2} + 2w - 1) + 2w \\ = {w}^{3} - {w}^{3} - 2 {w}^{2} + w + 2w \\ = - 2 {w}^{2} + 3w[/tex]
Some rules:
[tex]( + ) \times ( + ) \ = ( + ) \\ ( - ) \times ( + ) = ( - ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( - ) = ( + )[/tex]
Hope this helps...
Good luck on your assignment..
A baker is making cookies. She uses 3 cups of flour for every 8 oz of chocolate chips
How many cups of flour are needed with 192 oz of chocolate chips?
Answer: 72cups
Step-by-step explanation:
there are 8oz in a cup, so 8oz x 3cups = 24oz
[tex]\\ \frac{24}{8} \ = \frac{x}{192} \\(24) (192) = 8x\\(3) (192) = x\\576=x\\[/tex]
[tex]\frac{576}{8} = 72cups[/tex]
The baker will need 72 cups of flour for 192oz of chocolate chips.
The Mississippi River flows at a rate of 16,790 cubic meters per second. Choose the best approximation of the flow rate of the Mississippi River. Choose 1 answer: A:2 * 10^3 B: 2*10^4
Answer:
B, 2(10^4)
Step-by-step explanation:
2(10^3)= 2000
2(10^4)= 20000
2(10^4) Is closer to 16790 than 2(10^3)
What is the area of the triangle below?
3
16
O A. 24 sq. units
O B. 19 sq. units
O C. 48 sq. units
O D. 16 sq. units
Answer:
answer is 24
area of triangle=1/2 base*height
1/2*16*3=24
Answer:
24 sq. units
Step-by-step explanation:
Area of a triangle = Base x height ÷ 2
Base = 16
Height = 3
Therefore 16 x 3= 48 ÷2 = 24
I really hope this helps:)
This is probbaility, please just help me. i've been stuck forever!
Your answer would be 0.14 to the nearest hundredth.
The question P(Walk to school | Senior) is asking for the probability that a student walks to school given that they're a senior. Therefore we have to count how many total senior students there are, which is 35.
To form the probability, we then need to see how many of these 35 students walk to school, which we're given as 5. Thus, the probability is 5/35 which simplifies to 1/7.
1/7 as a decimal is 0.1429, which, when rounded to the nearest hundredth, gives us 0.14.
I hope this helps! Let me know if you have any questions :)
For every 1000 hits a channel gets it makes £16 from ad revenue. How much will the channel make from each hit?
Hi there! Hopefully this helps!
The answer is: 0.016
Here is how I got that answer:
16/1000=0.016
Answer:
Step-by-step explanation:
£16÷1000=0.016p
Pleas Help 9th grade work
Consider the reflectional symmetry of the shape.
How many lines of symmetry does the shape have?
2
3
4
5
Answer:
4.
Step-by-step explanation:
One line of symmetry is horizontal ( through the centre of the horizontal part of the cross).
Another is a vertical line through the centre of the vertical part.
Then there are 2 diagonal lines of reflectional symmetry.
How to do this question plz?
Answer:
Ratio of George age to Carl's age to Alex age = 1 : 12 : 4
Step-by-step explanation:
Let the age of Alex = A years
Age of George = G years
And age of Carl = C years
"Alex is 12 years older than George"
A = G + 12 ------(1)
"Carl is 3 times older than Alex"
C = 3A
C = 3(G + 12)
C = 3G + 36 ------(2)
"Sum of their ages is 68 years"
A + G + C = 68 ------(3)
By substituting the values of A and G in equation (3)
G + 12 + G + 3G + 36 = 68
5G + 48 = 68
5G = 20
G = 4 years
From equation (1),
A = 4 + 12 = 16 years
From equation
C = 3(4) + 36
C = 12 + 36
C = 48 years
Ratio of their ages = G : C : A
= 4 : 48 : 16
= 1 : 12 : 4
The probability of pulling out a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math
THIS IS THE COMPLETE QUESTION BELOW;
The probability of pulling a green marble out of a bag of colored marbles is 2:5. If you were to pull colored marbles out of the bag one at a time, and putting the marble back each time for 600 tries, approximately how many time would you select a green marble?? ( explanation too) 7th grade Math
Answer:
We would approximately pick a green marble 240 times
Step-by-step explanation:
Given from the question the probability of pulling a green marble out of a bag of colored marbles is 2:5
Let us denote the number of trials as X
Now the approximately number of times a green marble can be selected would be
=2/5 times
From the question we are given 600 trials
which implies our x=600
Therefore, the number of times we would pick a green marble is:
2/5 × 600 times
≈ 240 times
Therefore, we would approximately pick a green marble 240 times
Andre types 208 words in 4 minutes. Noah types 342 words and 6 minutes.who types faster explain?
Answer:
Noah
Step-by-step explanation:
Find how many words each person types in one minute. Andre types 208/4=52 words/min and Noah types 342/6=57 words/min. The answer is Noah.
Answer:
noah types faster
Step-by-step explanation:
Andre
208 words/ 4 minutes =
52 words per minute
Noah
342 words / 6 minutes = 57 words per minute