Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
What is distance?Distance is the overall length of a journey that a person, item, or vehicle takes to get from one place to another. Due to its scalar nature, it has simply magnitude and no direction. Typically, distance is expressed in terms of metres, kilometres, miles, or feet. It is distinct from displacement, which describes the shift in an object's location from its starting point to its ending point while also taking the movement's direction into consideration.
According to given information:We can start by using the formula:
distance = rate × time
Let's first consider the trip downstream. In this case, Ina's speed relative to the river current adds up to the distance traveled per unit of time. So we have:
16 = (x + y) × 2
Simplifying and solving for x + y, we get:
x + y = 8
Now let's consider the trip upstream. In this case, Ina's speed relative to the river current subtracts from the distance traveled per unit of time. So we have:
16 = (x - y) × 4
Simplifying and solving for x - y, we get:
x - y = 4
We now have two equations with two variables, so we can solve for x and y using either substitution or elimination. Let's use elimination:
(x + y) + (x - y) = 8 + 4
2x = 12
x = 6
Now we can substitute x = 6 into either of the original equations to solve for y. Let's use the first equation:
x + y = 8
6 + y = 8
y = 2
Therefore, Ina rows at a rate of 6 mph in still water, and the current flows at a rate of 2 mph.
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Select the correct answer.
Mary is buying several items that cost $128.25 total. She is using a store coupon for 35% off her purchases. She has to pay 4% sales tax. Calculate the total cost of the items.
A.
$80.03
B.
$83.36
C.
$86.70
The total cost of the several items that originally cost $128.25 with a coupon for 35% off and sales tax of 4% is C. $86.70.
How the total cost is determined:The original cost is discounted by 35% using a discount factor of 0.65 and increased by a sales tax factor of 1.04.
After the multiplications, the product shows the total cost that Mary incurred for buying the items.
Original cost of several items Mary is buying = $128.25
Coupon discount = 35%
Discount factor = 0.65 (100 - 35)
Sales tax rate = 4%
Sales tax factor = 1.04 (100 + 4)
The total cost of the items = $86.70($128.25 x 0.65 x 1.04)
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If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.
Answer:
Step-by-step explanation:
To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.
We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's find the length of each side of the triangle:
AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34
BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136
CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170
Now, let's check if the Pythagorean theorem is satisfied:
AC² = AB² + BC²
170 = 34 + 136
Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.
We know that,
the distance between two points=√(x2-x1)²+(y2-y1)²
∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²
=√(9+25)
= √(34)
∴ The length of side AB = √(34)
Again,
The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]
= √(100+36)
= √136
∴ The length of side BC =√136
Also,
The distance between points A and D, AC= √(-8-5)²+(3-2)²
= √(169+1)
= √170
∴ The length of side AC=√170
Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170
Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,
AC²=170
BC²=136
AB²=34
Clearly, 170=136+34
or, AC²=AB²+BC²
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Given Circle C, calculate the length of PQ (Thx for any help!)
Answer:
3π
Step-by-step explanation:
Given
Radius=9
Angle=60°
Since PQ is an arc
Perimeter of an Arc =(θ/360)×2πr
60/360×2π(9)
1/6×18π
3π
Based on a survey of 100 households, a newspaper reports that the average number of vehicles per household is 1.8 with a margin of error of ±0.3. The population surveyed is 50,000 households.
How many vehicles are included in the margin of error? Enter your answer in the blank.
Answer:
Step-by-step explanation:
The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).
To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:
0.3 * sqrt(100) = 3
So the margin of error in terms of the number of vehicles is ±3.
Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.
So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.
e) Write a proof to show AABC ~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
Answer:
Step-by-step explanation:
no
Can yall help me with this
Answer:
x = 67
Step-by-step explanation:
The two triangles are identail.
Answer:
x = 67
because 67 and x the same
James takes a 150000 mortgage for 20yrs and makes a monthly payment of 915.00. What percent of the total loan does he pay back?
James pays back approximately 82.33% of the total loan in interest over the 20-year period.
To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.
Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately
= 4.25% / 12
= 0.35% (4.25% annual rate divided by 12 months).
The monthly payment of $915.00 is comprised of both principal and interest.
In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.
To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months
20 years x 12 months/year = 240 months
and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.
To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:
$123,500 ÷ $150,000 x 100 ≈ 82.33%
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A vehicle purchased for $29800 depreciates at a constant rate of 7% per year. Determine the approximate
value of the vehicle 11 years after purchase.
Round to the nearest whole number.
The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413
Given data ,
Let the initial cost of the vehicle be = $ 29,800
Now , the rate of depreciation be r = 7 %
Let the number of years be n = 11 years
And , the exponential decay is given by the equation ,
x ( t ) = x₀ × ( 1 + r )ⁿ
On simplifying , we get
x ( 11 ) = 29800 ( 1 - 0.07 )¹¹
x ( 11 ) = 29800 ( 0.93 )¹¹
x ( 11 ) = 13,413.085
Hence , the cost of the vehicle after 11 years is A = $ 13,413
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Step-by-step explanation:
x = -2 or x = 2
x + 2 = 0 or x - 2 = 0
(x + 2) (x - 2) = 0
x² - 4 = 0
#CMIIWFind the probability that
event A or B takes place.
Probability that event A or B takes place is, P(A or B) = 16/21.
Here from the Venn diagram we can obtain that,
Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21
Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21
Probability of occurring event A and event B both = 4/21
So, P(A) = 6/21
P(B) = 14/21
P(A and B) = 4/21
We know that the union of events formula,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 6/21 + 14/21 - 4/21
P(A or B) = (6 + 14 - 4)/21
P(A or B) = 16/21
Hence the value of P(A or B) = 16/21.
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You deposit $300 each month into an account earning 2% interest compounded
monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
a) The future value of the account after 30 years can be calculated using the formula:
FV = P * ((1 + r/n)^(n*t))
where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:
FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60
So you will have $150,505.60 in the account after 30 years.
b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:
$300 * 360 = $108,000
c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:
$150,505.60 - $108,000 = $42,505.60
Answer:
a) you will have approximately $133,381.85 in the account in 30 years.
b) a total of $108,000 into the account over 30 years.
c) a total of $25,381.85 in interest over 30 years.
Step-by-step explanation:
A study found that 18% of dog owners brush their dogs teeth. Of 639 owners, about how many would he expected to brush their dog’s teeth? Explain
To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).
Expected number of dog owners who brush their dog's teeth = 639 x 0.18
= 115.02 (rounded to the nearest whole number)
So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.
I need help with this please.
1/2 x 3 x 3 = 4.5
I just need help on how 4.5 is the answer.
Answer:
3
Step-by-step explanation:
3 * 3 = 6
1/2 * 6 = 3 not 4.5
Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.
The 3 x 3 part turns into 9
So we have 1/2 x 9 or 9/2
Use long division to find that 9/2 gives a quotient of 4 and remainder 1
Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.
The "remainder 1" then leads to 1/2 = 0.5
quotient = 4
remainder = 1 ---> decimal portion = 1/2 = 0.5
So that's how we get to 4+0.5 = 4.5
You can use a calculator to see that 9/2 = 4.5
Find an angle in each quadrant with a common reference angle with 285°, from 0°≤θ<360
The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°
Understanding QuadrantA common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.
For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.
Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:
First Quadrant: An angle in the first quadrant with a reference angle of 15° is 15° itself.Second Quadrant: An angle in the second quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180°. Therefore, an angle in the second quadrant with a common reference angle with 285° is 180° - 15° = 165°.Third Quadrant: An angle in the third quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180° and then adding 180°. Therefore, an angle in the third quadrant with a common reference angle with 285° is 180° + 15° = 195°.Fourth Quadrant: An angle in the fourth quadrant with a reference angle of 15° can be found by subtracting the reference angle from 360°. Therefore, an angle in the fourth quadrant with a common reference angle with 285° is 360° - 15° = 345°.Learn more about quadrant here:
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a shape has 3 sides. the bottom edge is 5 inches and the hight is 1 foot. what is the surface area
Answer:
Step-by-step explanation:
What is the maximum possible product of two numbers that have a sum of -8?
The maximum possible product of two numbers that have a sum of -8 is 16.
How to find the maximum possible product of two numbers that have a sum of -8Let us name the two numbers "x" and "y".
We are aware of the following: x + y = -8
We're looking for the greatest possible product of x and y.
The number we're looking that are as near together as feasible and have a sum of -8.
-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.
The sum of these two figures is:
x * y = (-4) * (-4) = 16
So, the maximum possible product of two numbers that have a sum of -8 is 16.
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Please solve quickly will give brainlest if correct!!!!!
The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Writing the sum using the sigma notationFrom the question, we have the following parameters that can be used in our computation:
[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]
From the above expression, we can see that the different expression in each term is
9/n
So, we introduce a variable
Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
When represented using the sigma notation, we have
[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]
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You are asked to advise Alpha Tire Co. on the feasibility of offering a 35,000-mile warranty on their tires. At this time Alpha Tire believes the mean time to failure is 40,000 miles
µ
with standard deviation of miles to failure at 3700 or
. If a free replacement warranty is offered, promising that the tires will last for at least 35,000 miles, what proportion of tires would qualify for the free replacement because they are expected to fail while they were still covered by the warranty? In light of your finding, what advice would you give to Alpha Tires about a warranty for a free tire replacement if the tires fail before 35,000.
Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.
Why is this so ?Using a standard normal distribution table or calculator, we can find the z scores corresponding to 35,000 miles and 40,000 miles...
z 1 = ( 35,000 - 40,000) / 3,700 = -1.35
z 2 = (40,000 - 40,000) / 3,700 = 0
Then, we can find the area between these z scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:
P( -1.35 < Z < 0) = 0.4119 or 41.19%
What it means is that , about 41.19% of the tires would qualify for a free replacement.
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can someone help me please
here is the picture is about Row Ops
The result of engaging in the row multiplication operation in a matrix would be [ 1 /2 0 | 3 / 4 ]
[ -1 5 | 4 ].
How to multiply matrices ?First, you should multiply the first row by the value given of 1 / 4 to be:
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
Then you can replace the values found by the values in the matrix to be :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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the front of a refrigerator with a freezer on the bottom . The freezer part on the bottom has a height of 2 feet. The top part has a height of 5 feet.Explain how you find the total area of the front of the frig
The total area of the front of the figure is 21 [tex]feet^{2}[/tex].
What is the area?
The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.
To find the total area we need to add the area of the refrigerator and the area of the freezer.
The top part i.e refrigerator has a height of 5 feet and 3 feet width
Area of the refrigerator section = height * width
= 5 * 3
= 15 [tex]feet^{2}[/tex]
The bottom part i.e freezer has a height of 2 feet and 3 feet width
Area of the refrigerator section = height * width
= 2 * 3
= 6 [tex]feet^{2}[/tex]
The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section
= 15 + 6 = 21[tex]feet^{2}[/tex]
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Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be 2.79 N/cm³
What is a trapezium?A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.
Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..
Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be:
= 834 / 299.25
= 2.79 N/cm³
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Answer:
1.54
Step-by-step explanation:
Trapezium=
12+24=36
36 x (length) 15 = 540cm^2
Pressure= force/area
832/540 = 1.54N/cm^2
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25.
The cost of each chair and table is $2.5 and $8.75 respectively.
Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.
We need to find the cost of each chair and table,
Let the cost of each chair and table be x and y respectively,
3x+2y = 25.......(i)
5x+6y = 65.........(ii)
Multiply the equation (i) by 3 and subtract ii from i,
9x+6y = 75 - (5x+6y = 65)
4x = 10
x = 2.5
Put x = 2.5 in any equation to find the value of y,
3(2.5)+2y = 25
2y = 17.5
y = 8.75
Hence, the cost of each chair and table is $2.5 and $8.75 respectively.
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Help pls i dont understand this
The percentage increase in the number of water bottles the company manufactured from February to April is 19%.
How to find the percentage increase ?In March, the company manufactured 7% more water bottles than in February:
Number of water bottles in March = 4,100 + 7% of 4,100
Number of water bottles in March = 4,387
In April, the company manufactured 500 more water bottles than in March:
Number of water bottles in April = 4,387 + 500
Number of water bottles in April = 4,887
To find the percent increase from February to April, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
percent increase = (4,887 - 4,100) / 4,100 * 100%
percent increase = 787 / 4,100 x 100%
percent increase = 19%
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Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, what was the reserve rate? And what are the steps to solve?
Tthe reserve rate was approximately 0.9434, or 94.34%.
How to solve for the reserve rateThis is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:
sum = a(1 - r^n) / (1 - r)
where a = 3000r is the first term.
As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:
3000r/(1-r) = 50,000
Solving for r, we get:
r = (50,000)/(3000 + 50,000) = 0.9434
Therefore, the reserve rate was approximately 0.9434, or 94.34%.
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Some varsity soccer players are paired with a junior varsity (JV) player for training purposes: 2/3 of the varsity are partnered with 3/5 of the JV. What fraction of the players are partnered for training?
Let's say there are $v$ varsity players and $j$ JV players.
The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:
$\sf\implies\:(2/3)v$
And the number of JV players partnered with a varsity player is:
$\sf\implies\:(3/5)j$
Since these two numbers represent the same group of paired players, they must be equal:
$\sf\implies\:(2/3)v = (3/5)j$
To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:
$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired
$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired
So the total fraction of players who are paired is:
$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)
Simplifying:
$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$
Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answer:
B) The other number is even.
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a radius of 4 feet and a height of 18 feet. Container B has a radius of 5 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
The percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
What is volume of cylinder?[tex]V = r^2h[/tex] , where r is the radius of the cylinder's base, h is its height, and (pi) is a mathematical constant corresponding roughly to 3.14159, gives the volume of a cylinder.
To solve this problem, we need to calculate the volumes of the two containers and then determine how much of Container B is empty after the water from Container A is transferred to it.
The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex] , where r is the radius of the base and h is the height of the cylinder.
Container A has a radius of [tex]4[/tex] feet and a height of 18 feet, so its volume is:
[tex]V(A) = \pi (4^{2} )(18) = 288\pi[/tex] cubic feet
Container B has a radius of 5 feet and a height of 15 feet, so its volume is:
[tex]V(B) = \pi (5)^2(15) = 375\pi[/tex] cubic feet
When the water from Container A is transferred to Container B, the volume of water in Container B will be:
V(water in [tex]B) = V(A) = 288\pi[/tex] cubic feet
The total volume of Container B is 375π cubic feet, so the volume that is empty after the transfer is:
V(empty in [tex]B) = V(B) - V(water in B) = 375\pi - 288\pi = 87\pi[/tex] cubic feet
To find the percentage of Container B that is empty, we need to divide the volume that is empty by the total volume of Container B and then multiply by 100:
Percent empty [tex]= (V(empty in B) / V(B)) \times 100[/tex]
[tex]= (87\pi / 375\pi) \times 100[/tex]
[tex]= 23.2[/tex]%
Therefore, the percent of Container B that is empty after the pumping is complete, to the nearest tenth, is [tex]23.2[/tex]%.
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Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
How to solveA polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:
f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]
Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:
f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
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3. Point F(21, -14) is rotated-90° clockwise about the origin. What are the coordinates of F’
Answer: The coordinates of F' are (14, 21).
Step-by-step explanation:
Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.
(21, -14) ➜ (14, 21)
The coordinates of F' are (14, 21).
for question 6 is wax and yau are verticle or not
In the given diagram, angle WAX and angle YAU are vertical angles
What are vertically opposite angles?From the question, we are to determine if angles WAX and YAU are vertical angles or not
Vertically opposite angles are pairs of angles that are opposite each other and formed by the intersection of two straight lines.
When two straight lines intersect, they form four angles at the point of intersection. Vertically opposite angles are the angles that are opposite each other, that is, they are located on opposite sides of the intersection point and are formed by the pair of opposite rays.
Vertically opposite angles are congruent, which means that they have the same angle measure. This property holds true for any pair of vertically opposite angles, regardless of the angle size or the orientation of the lines.
Hence, angle WAX and angle YAU are vertical angles
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