Answer:
573.95 gallons/minute
Step-by-step explanation:
To find the amount of oil after 12 minutes you take the difference between the amount of oil that flows into the tank minus the the oil that flows aout the tanks. Then you have:
[tex]T(t)=F(t)-E(t)\\\\F(t)=t^2+\frac{1}{t+1}\\\\E(t)=\frac{ln(t+7)}{t+2}[/tex]
Being F(t) the flow that goes into the tank per minute, and E(t) the amount of oil that flows outside the tank per minute.
To know the total amount of F and E for t=12 you integrate these function:
[tex]\int_0^{12}F(t)dt=\frac{t^3}{3}+ln(t+1)|_{0}^{12}=578.56\frac{gallons}{minute}\\\\\int_{0}^{12}E(t)dt=\int_0^{12}[\frac{ln(t+7)}{t+2}]dt=4.61\frac{gallons}{minute}\\\\\int_0^{12}T(t)dt=578.56-4.61=573.95\frac{gallons}{minute}[/tex]
573.95 gallons/minute
(11+i)^2
please help!
Answer:
121 + 22i - 1
Step-by-step explanation:
Expand:
(11 + i)² = (11 + i)(11 + i)
Note that:
i² = -1
Use FOIL method. Multiply first terms, outside terms, inside terms, then the last two terms:
(11)(11) = 121
(11)(i) = 11i
(i)(11) = 11i
(i)(i) = -1
Combine like terms:
121 + 11i + 11i - 1
121 + (11i + 11i) - 1
121 + 22i - 1
121 + 22i - 1 is your answer.
~
Andrea has a credit score of 895 and Ashley has a credit score of 768. Stutts National Bank has determined that both will receive a credit card; however, the borrower with the lower credit score will be charged a $50.00 fee the first time she makes a purchase. If both receive a credit card with $1,500.00 available credit, what will Ashley's remaining available credit be after she purchases a $425.00 Coach bag?
Answer:
Ashley's remaining available credit after her first purchase is $1025.00
Step-by-step explanation:
Here we are told that the borrower with the lower credit score will be charged $50.00 fee after the first purchase
Therefore, we have
Credit score Andrea = 895
Credit score for Ashley = 768
Therefore, Ashley has the lower credit score hence after her first purchase of a $425.00 Coach bag, we have
Available credit = Initial balance - Purchase - Charges
∴ Available credit = $1,500.00 - ($425.00 + $50.00) = $1025.00
Therefore, Ashley's remaining available credit after she purchases the $425.00 Coach bag = $1025.00.
Which three-dimensional figures have lateral faces that are polygons? Check all that apply
Question:
Which three-dimensional figures have lateral faces that are polygons? check all that apply.
- cones
- cylinders
- hemispheres
- prisms
- pyramids
- spheres
Answer:
The correct choices are;
- prisms and
- pyramids
Step-by-step explanation:
A polygon is a figure closed or bounded with several straight line segments and polygons are named based on how many sides, side size and sizes of angles that they have present.
A three sided polygon for example is called a triangle
A lateral face are the faces of a prism except the base
Based on the definitions, we note that out of the options, only prisms, and pyramids have lateral faces that are made up entirely of straight line segments, hence polygons. Therefore, the correct choices are prisms and pyramids.
Answer:
Actually the correct is Cylinders, Prisms, and Pyramids. I just did it
Step-by-step explanation:
10 1/12 + 6 2/3 =
(ANSWER SIMPLIFIED & AS MIXED NUMBER!)
Answer:
16 3/4 orrrrrrrr 67/4
Step-by-step explanation:
10 1/12 + 6 8/12
you need to change the denominators to be the same so you can add them
PLZ HELP ON THIS QUESTION ASAP PLZ THANKS AND 5 STARS AND WHEN THERES OPTION FOR BRAINLEST ILL GIVE YOU BRAINLEST ASAP WITH ANSWER PLZ 15 POINTS
Answer:
£114
Let me know if it is incorrect so that I can review my answer and fix it! :)
Step-by-step explanation:
20% * £1200 = £240
£1200 + £240 = £1440
£1440 - £300 = £1140
£1140 / 10 = £114
Answer:
£114
Step-by-step explanation:
Total to be paid:
[1200 + (20% of 1200)] - 300
[1200 + (20/100 × 1200)] - 300
1200 + 240 - 300
1140
10 installments
Each:
1140/1
114
Suppose vanilla beans cost $600 per kilogram. Julie bought 9 grams of vanilla beans. Jacques bought 70 grams of vanilla beans. How much more did Jacques pay for his vanilla beans? $5.40 $12.00 $36.60 $42.00
Answer:
5.40
Step-by-step explanation:
Cost of 70 gram vanilla beans is $42, so Jacques pay $42 for his vanilla beans.
Cost based problem:What information do we have?
Cost of 1 kg vanilla beans = $600
Amount of vanilla beans bought by Jacque = 70 gram
Cost of 1 g vanilla beans = [600/1000]
Cost of 1 g vanilla beans = $0.6 per gram
Cost of 70 gram vanilla beans = 70 × Cost of 1 g vanilla beans
Cost of 70 gram vanilla beans = 70 × $0.6
Cost of 70 gram vanilla beans = $42
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ANSWER FAST I NEED IT TO PASS Follow the steps to solve the equation using the algebra tiles.
−4x + 1 = x + (−4)
1. Add 4 positive x-tiles to both sides and create zero pairs.
2. Add 4 positive unit tiles to both sides and create zero pairs.
3. Divide the unit tiles evenly among the x-tiles.
x =
The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
-4x + 1 = x + (-4)
Add 4 positive x-tiles to both sides and create zero pairs:
-4x + 1 + 4x = x + (-4) + 4x
1 = 5x - 4
Add 4 positive unit tiles to both sides and create zero pairs:
1 + 4 = 5x - 4 + 4
5x = 5
Divide the unit tiles evenly among the x-tiles:
5x/5 = 5/5
x = 1
The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1
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x = 1
Step-by-step explanation: did on edge
what’s equivalent for x to the power of -3 that uses positive exponents?
A. x to the power of -3
B. x to the square root of 3
C. 1 over x to the power of 3
D. 1 over x to the power of 1/3
Answer:C
Step-by-step explanation:
When using negative exponents, I’m you flip the number to the opposite side numerator to denominator in this case. So you would have 1 over x to the third power.(1/x^3)
The width of a swimming pool is 12 feet less than the pool's length. The area of the pool is 540 square feet. What are the dimensions of the pool?
Answer:
30 feet by 18 feet
Step-by-step explanation:
Area = length * width
A = x*w
w = x - 12
A = 540 sq. ft
540 = x * (x -12)
x*x - 12x - 540 = 0
x*x - 12x + 36 - 36 - 540 = 0
(x - 6)^2 - 576 = 0
x - 6 = 24
or x -6 = -24
x = 30 or x = -18
w = 30 - 12 = 18
30 ft by 18 ft
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with multiplicity 27
O
f(x) = 2(x + 7)(x + 5)(x-2)
Rx) = 2(x - 7)(x - 5)(x + 2)
Rx) = (x + 7)(x + 5)(x + 5)(x - 2)
f(x) = (x - 7)(x - 5)(x - 5)(x + 2)
The polynomial function with a leading coefficient of 1 and the specified roots and multiplicities is f(x) = (x + 2)(x - 7)(x - 5)^27.
Explanation:The polynomial function you are looking for, which has a leading coefficient of 1, roots at -2 and 7 each with a multiplicity of 1, and a root at 5 with multiplicity 27, is given by the expression:
f(x) = (x + 2)(x - 7)(x - 5)^27
The given roots indicate the factors of the polynomial, and the multiplicity of each root shows how many times that factor is repeated. Hence, the root -2 becomes (x + 2), the root 7 becomes (x - 7), and the root 5 with multiplicity 27 becomes (x - 5)^27. The leading coefficient is 1, which means these factors are not multiplied by any other constant.
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HELP WITH MY MATHS HOMEWORK, ITS A YEAR 7 QUESTION
Which of these are expressions?
298
22 x 3
7x = 63
a + b + c
0
Step-by-step explanation:
An expression is something like 7x=63
Find the volume of the figure
Answer:
see below
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the diameter so we need the radius
r = d/2 =13/2 = 6.5
V = pi (6.5)^2 (19)
V = 802.75 pi mm^3
We can approximate pi by 3.14
V =2520.635 mm^3
or by using the pi button
V =2521.913503 mm^3
Determine the longest side in ΔDEF.
A) segment EF
B) segment DE
C) segment FE
D) segment DF
Look at the graph of the linear function.The rate of change between point A and point B is 2. What is the rate of change between point C and point D?
–2
Negative one-half
One-half
2
the answer is be like 20
Answer:
The answer is -1/2
Step-by-step explanation:
Use the line plots to answer each question.
1) The line plot below shows the sizes of
different insects (in inches).
What is the difference in size between the
shortest and longest insect?
Write one digit on each side of 92 to make a four digit multiple of 45. How many different solutions does this problem have?
Answer:
Two solutions:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
Step-by-step explanation:
The multiples of 45 always have as last digit 0 or 5, so the digit to the right of 92 has to be 0 or 5.
If we use 0 as the last digit, our options of multiples will be just 7920 (7920 = 45 * 176)
If we use 5 as the last digit, our option of multiples will be just 2925 (2925 = 45 * 65)
So we have just two solutions for this problem:
Adding 7 to the left and 0 to the right: 7920
Adding 2 to the left and 5 to the right: 2925
The grades on a history midterm at Almond are roughly symmetric with \mu = 85μ=85mu, equals, 85 and \sigma = 2.0σ=2.0sigma, equals, 2, point, 0. Michael scored 868686 on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Answer:
0.50
Step-by-step explanation:
The z-score for Michael's exam grade is 0.5.
Explanation:To find the z-score for Michael's exam grade, we can use the formula: z = (x - µ) / σ, where x is the value of Michael's grade, µ is the mean, and σ is the standard deviation.
Plugging in the given values,
we get z = (86 - 85) / 2 = 0.5.
Therefore, the z-score for Michael's exam grade is 0.5.
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A line passes through the points (-1, 4) and (2, -2). What is the equation of this line?
Write your answer in the form y=mx+b.
I don't get it please help!
Answer:
y = -2x+2
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
= (-2-4)/(2--1)
= (-2-4)/(2+1)
-6/3
-2
We have the slope =-2
We can substitute it into the equation
y = mx+b where m is the slope and b is the y intercept
y =-2x+b
Use a point for x and y to solve for b
4 = -2(-1) +b
4 = 2+b
Subtract 2 from each side
4 -2 = -2+2+b
2 = b
We know m and b
y = -2x+2
Answer:
y = -2x + 2
Step-by-step explanation:
Slope: (-2-4)/(2--1) = -6/3 = -2
y - 4 = -2(x - -1)
y = -2x - 2 + 4
y = -2x + 2
A number, y, is equal to twice the sum of a smaller number and 3. The larger number is also equal to 5 more than 3 times the smaller number. Which equations represent the situation? 2 x minus y = negative 6 and 3 x minus y = negative 5 2 x minus y = negative 3 and 3 x minus y = negative 5 2 x minus y = negative 6 and x minus 3 y = 5 2 x minus y = negative 3 and x minus 3 y = 5
Answer:
2 x minus y = negative 6 and 3 x minus y = negative 5
Step-by-step explanation:
y = 2(x+3) = 2x + 6 or 2x - y = -6
y = 5 + 3x or 3x - y = -5
The equations that represent the situation is: 2 x minus y = negative 6 and 3 x minus y = negative 5
From the given information:
Let the smaller number be x; then the word problem can be expressed as:
y = 2(x + 3) ---- (1)y = 5 + 3x ---- (2)From (1), if we open the brackets, we have:
y = 2x + 6-2x + y = +6multiplying through by (-), we have:
2x - y = -6Also, from equation (2)
y = 5 + 3xBy rearrangement
y - 3x = 5-3x + y = 5Multiplying through by (-), we have:
3x - y = -5Therefore, we can conclude that the equations that represent the situation is: 2 x minus y = negative 6 and 3 x minus y = negative 5
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Find the HCF of 168 and 196.
Answer:
The HCF of 168 & 196 is 28
Step-by-step explanation:
The factors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, 196
The highest factor that both 168 and 196 share is 28
Hope this helps :D
Answer:
28
Step-by-step explanation:
168 = 2³ × 3 × 7
196 = 2² × 7²
HCF(168 ; 196) = 2² × 7 = 4 × 7 = 28
A fast food restaurant wants to know what types of toys to put in their kids meals, so they will survey their customers. What would be the BEST way to do this?
personally i would ask every one who orders a kids meal.
hope this helps
Answer:
the answer is c) Ask anyone who orders a kid's meals
Step-by-step explanation:
David is buying a cheese wheel priced at $650 before tax. The store charges 8%, percent sales tax.
What is the total price, including tax, David pays for the cheese wheel?
Answer:
Pretty sure it would end up being $702 including tax
Step-by-step explanation:
650 * 0.08 = 52
52 + 650 = 702
18,300 divided by 19.7%
Answer:
13,300 divided by 19.7 % is 92893.4010152
Step-by-step explanation:
Find the mode of this data set
18.33.25,36,35,31, 19, 30,23,28.33
Answer:
33
Step-by-step explanation:
So I just put them in order....18,19,23,25,28,30,31,33,33,35,36
and you can see that 33 pops up twice when the others only pop up once..so the answer is 33
An angle measures 50° more than the measure of its supplementary angle. What is the measure of each angle?
An angle measures 50° more than the measure of its supplementary angle. However, there are no angles that satisfy this condition.
Explanation:An angle measures 50° more than the measure of its supplementary angle.
To solve for the measure of each angle, we can set up an equation:
Let x be the measure of the angle, and let y be its supplementary angle.
Since the sum of the measures of two supplementary angles is 180°, we can write the equation:
x = y + 50°
Substituting y + 50° for x in the equation, we get:
y + 50° = y
Subtracting y from both sides, we get:
50° = 0
Since there is no solution to this equation, it means that there are no angles that satisfy the given condition.
The smaller angle measures 65° while the larger angle measures 115°.
Let's denote the measure of the smaller angle as x degrees. Since the angles are supplementary, their sum must be 180 degrees. Thus, the measure of the larger angle will be (x + 50) degrees.
Using this information, we can form the following equation:
x + (x + 50) = 180
Simplify the equation:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide both sides by 2:
x = 65
Therefore, the measures of the angles are:
Smaller angle: 65°Larger angle: 115° (because 65° + 50° = 115°)help please!! kinda confusing for me...
6
Step-by-step explanation:
-2^3=-8
-10+(-8)=-10-8=-18
-18÷-3=6
What is answer 6x+7-5x=10
Answer:
i think the answer is going to be 3
Step-by-step explanation:
Which number is the additive inverse of –5? – One-fifth 0 Negative one-fifth 5
Answer:
The additive inverse is 5
Step-by-step explanation:
What to we add to -5 to get it to be 0
-5 +x = 0
We add 5
-5+5 =0
Answer:
It is five
Step-by-step explanation:
Which statement is true about the equation (x – 4)(x + 2) = 16?
The equation x - 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 - 2x - 8 = 0.
The factored form of the equation is (x + 4)(x – 6) = 0.
One solution of the equation is x=-6.
Answer:
The factored from of the equation is (x+4)(x-6)=0.
Step-by-step explanation:
When solving this problem, we need to find the factored form of this problem. Remember that in factored form, the right-hand side of the equation must equal to 0.
We can simply convert the left-hand side to standard form first:
(x-4)(x+2)=16 --> x²-2x-8= 16.
Now, to set the right-hand side of the equation to 0, we must subtract -16 from both sides:
x²-2x-24=0.
Now, if we convert this to factored form, we will get:
(x+4)(x-6)= 0.
All of the other statements are false. This is the only true statement.