The surface area of the tank is 7038 square inches
The surface area can be calculated as follows
The diameter is 28 inch
radius= diameter/2
= 28/2
= 14
Height= 66 inch
The surface area can be calculated as follows
2πrh + 2πr²
= 2(3.142)(66) + 2(3.142)(14²)
= 5806+2(616)
= 5806+1232
= 7038 square inches
Hence the surface area of the tank is 7038 square inches
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By using the knowledge acquired about proportional relationships, solve the following questions.
Does it represents a proportional relationship?
find the constant of proportionality (K=Y/X)
give the equation that represents the relationship (Y=K*X)
The relationships represent proportional relationships and the constant of proportionalities are 5/7 and 12
The graphDoes it represent a proportional relationship?
Yes, the graph represents a proportional relationship
This is so because the graph is a linear equation and it passes through the origin
How to find the constant of proportionality (K=Y/X)
On the graph, we have the following point
(X, Y) = (28, 20)
So, we have
K = 20/28
Evaluate
K = 5/7
How to determine the equation that represents the relationship (Y=K*X)Here, we have
Y = K * X
This gives
Y = 5/7X
The tableDoes it represent a proportional relationship?
Yes, the table represents a proportional relationship
This is so because the table is a linear equation and it has a value (0, 0)
How to find the constant of proportionality (K=Y/X)
On the graph, we have the following point
(X, Y) = (5, 60)
So, we have
K = 60/5
Evaluate
K = 12
How to determine the equation that represents the relationship (Y=K*X)Here, we have
Y = K * X
This gives
Y = 12X
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You have decided to buy a new home and the bank offers you a 30 year fixed loan at 5.5% on a balance of $150,000. Use the table provided to determine the monthly payments. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $416.67 c. $852.00 b. $439.00 d. $874.32
The monthly payment become $852. Thus , option C is correct option.
According to the statement
We have to find that the monthly repayment.
So, For this purpose, we know that the
The monthly payment is the amount paid per month to pay off the loan in the time period of the loan.
From the given information:
You have decided to buy a new home and the bank offers you a 30 year fixed loan at 5.5% on a balance of $150,000.
Then
we know that the:
Monthly payment = Amount / discount factor
And discount factor = 1-(1+i)^-n / i
Then
M = A*i/1-(1+i)^-n
Where, A=$150000
r=5.5%=0.055
i = 0.555/12
i = 0.004
And t = 30 year
n = 30*12
n = 360
Substitute all the values,
M = 150000*0.004/ 1-(1+0.004)^-360
M = 687.5 / 1-0.192
M = 687.5 / 0.80722
M = 851.7
Approximately, Monthly payment is $852.
So, The monthly payment become $852. Thus , option C is correct option.
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Triangle ABC is similar to triangle DEF.
Side AB is the longest side of ABC and measures 12 cm.
Side DE is the longest side of DEF and measures 8 cm
Scale factor that takes triangle ABC to triangle DEF = 2/3
Scale factor that takes triangle DEF to triangle ABC = 3/2
How to Find the Scale Factor?Scale factor = side length of new figure/corresponding side length of original figure.
Given:
AB = 12 cmDE = 8 cmTriangles ABC and DEF are similar triangles.Scale factor that takes triangle ABC to triangle DEF = 8/12
Scale factor that takes triangle ABC to triangle DEF = 2/3
Scale factor that takes triangle DEF to triangle ABC = 12/8
Scale factor that takes triangle DEF to triangle ABC = 3/2
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PLEASE HELP!!!!
Groups of students are measuring the masses of several rocks. They have a scale that can show readings in pounds or kilograms. The teacher requires that they all make their measurements in kilograms.
Why would the teacher make a decision like this?
Choose 1 answer:
(Choice A)
A kilogram is larger than a pound, so the scale could measure more massive rocks.
(Choice B)
Accurate measurements cannot be made in pounds.
(Choice C)
Pounds cannot be converted to kilograms.
(Choice D)
It is easier to compare measurements when using the same unit system.
The teacher will make a decision like this because D. It is easier to compare measurements when using the same unit system.
How to explain the information?It should be noted that in this case, the students are measuring the masses of several rocks and they have a scale that can show readings in pounds or kilograms. The teacher requires that they all make their measurements in kilograms.
It should be noted that the teacher will make a decision like this because it is easier to compare measurements when using the same unit system.
Therefore, the correct option is D.
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A number times its opposite, increased by seven
????????????????????????????????
help asap please! 100 points!
Answer: u have to subtract 78-32 and divide by 100
Step-by-step explanation:
find the general form of the quadratic function with the vertex (1,4) and a point on the graph (-3,20)
The general form of the quadratic function is x² - 2 · x - y + 5 = 0.
How to find the general form of the quadratic function
In this question we must derive the equation of the parabola in vertex form, whose description is shown below:
4 · p · (y - k) = (x - h)² (1)
Where:
(h, k) - Coordinates of the vertex.(x, y) - Coordinates of a point of the parabola.p - Distance from vertex to focus.If we know that (h, k) = (1, 4) and (x, y) = (- 3, 20), then the distance from vertex to focus is:
p = (x - h) / [4 · (y - k)]
p = (- 3 - 1)² / [4 · (20 - 4)]
p = (- 4)² / 64
p = 16 / 64
p = 1 / 4
Then, the equation of the parabola in vertex form is y - 4 = (x - 1)². And now we find the general form of the quadratic formula, that is:
A · x² + B · x + C · y + D = 0 (2)
Then, we proceed to obtain the general form:
y - 4 = (x - 1)²
y - 4 = x² - 2 · x + 1
x² - 2 · x - y + 5 = 0
The general form of the quadratic function is x² - 2 · x - y + 5 = 0.
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Three-tenths of the books in the school library are how-to books. Of these, 0.2 deal with carpentry and 0.4 deal with electronics. Interpret what the figure 0.12 represents in this context.(1 point)
Responses
the fraction of the books in the library that are how-to books on electronics
the fraction of books in the library that are how-to books on carpentry
the fraction of the how-to books that are about either carpentry or electronics
the fraction of books in the library that are how-to books
The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.
What is the best interpretation of the figure 0.12 according to the information given in the task content?It follows from the task content that the best interpretation of 0.12 is to be determined.
On this note, since three-tenths of the books in the school library are how-to books, and of those, 0.4 deal with electronics;
The statement above therefore means that the fraction of books which are how-to books and deal with carpentry can be evaluated as;
= (3/10) × 0.4
= 0.3 × 0.4
= 0.12.
Ultimately, The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.
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Tony buys a washing machine.
20% VAT is added to the price of the washing machine.
Tony then has to pay £480
What is the price of the washing machine with no VAT added?
Total marks: 2
Answer:
384
Step-by-step explanation:
480x20%=96
480-96=384
Simplify (c4)−5.
1 over c
c
1 over c raised to the twentieth power
−c20
The expression is simplified to 1 over c raised to the twentieth power. Option C
What are index forms?The index form of a number can be defined as the number written as an exponential expression.
It is expressed as a single number raised to another number.
Another name for index form is standard form or scientific notation.
Index notation is also a way of representing variables or constants multiplied by themselves a number of times.
Example of index forms are:
a²
b³
c²
From the information given, we have to simplify
(c^4)^−5
Using the rule of indices, we have to multiply the powers
c^-20
Thus, the expression is simplified to 1 over c raised to the twentieth power. Option C
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Answer:
1 over c raised to the twentieth power
Step-by-step explanation:
Determine whether the relation is a function.
H={(6, - 2), (5,- 2), (4, -2), (3, - 2), (2, - 2)}
Yes, the relation is a function.
What does the term "relation function" mean?
In mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets. In arithmetic, a relation is called a function if it connects each element of the domain to a single element of the codomain. A relation could be a function or it could not.What is a relation simple definition?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.H={(6, - 2), (5,- 2), (4, -2), (3, - 2), (2, - 2)}
In a function, an x value can never repeat.
This is basically the only rule (that I know of), so, the given values can represent a function.
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Please help me understand the zero factor property with this problem. I understand the property when the equations have parentheses, but not when they don’t. I know the answer I just need help explaining! Thank you!
Two ways to do this! There are some more but these are the most intuitive.
Way 1: Factoring
You can factor this equation into one with parentheses. A way I like thinking of doing this is by seeing if you can split the coefficient of the middle term into the sum of two numbers, which, when multiplied with each other, equal the third term. To see what I mean, look at the equation you gave.
[tex]x^2 - 18x + 77 = 0[/tex]
[tex]x^2 - 7x - 11x + 77 = 0[/tex]
We notice that when -7 and -11 are multiplied, they equal 77. This means we can factor the equation! As follows:
[tex](x-7)(x-11)=0[/tex]
If you want to see why this works, cross-multiply out [tex](x-7)(x-11)[/tex]. You should see that it is equal to [tex]x^2 - 7x - 11x + 77[/tex].
From here, you should be able to see the solutions are [tex]x = 7, 11[/tex].
Way 2: Complete the Square
We can do something like this:
[tex]x^2 - 18x + 77 = 0\\x^2 - 18x + 81 = 4\\(x-9)^2 = 4\\x-9 = \pm\sqrt{4}\\x = 9\pm 2\\x = 7, 11[/tex]
Essentially, what we are doing is we are adding / subtracting from both sides of the equation so the left side becomes a perfect square of some term [tex](x-a)[/tex]. From there, we can just solve for [tex]x[/tex].
Hope this helps you, please let me know if anything confuses you.
manuel hace los 3/7 de la tarea mientras su compañero csarlos hace solamente los 4/5 de lo que hizo manuel. que parte de la tarea hizo carlos
The fraction is 12/35.
How to compute the fraction?From the information, it was stated that Manuel does 3/7 of the task while Carlos did 4/5 of what Manuel did.
Therefore, the fraction that was done by Carlos will be:.
= 4/5 × 3/7
= 12/35
The fraction is 12 / 35.
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6. Nancy deposits $1,200 into an account that pays 1.7% interest,
compounded
monthly. What is her ending balance after 1 year? Round to the nearest cent.
A. $1220.56
B. $1420.65
C. $1350.75
D. $1250.35
Based on the amount deposited by Nancy into the account and the interest it paid, the ending balance after 1 year is $1,220.40
How to find the ending balance?The ending balance of the amount that Nancy deposited which was $1,200 is based on the interest compounded on the amount over the investment year.
The ending balance can be found as:
= Amount deposited x ( 1 + rate) ^ number of years
Solving for the ending balance gives:
= 1,200 x (1 + 1.7%) ^ 1
= 1,200 x 1.017
= $1,220.40
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One number is three less than a second number. Four times the first is 10 more than 6 times the second. Find the
numbers.
***
Step-by-step explanation:
x = y - 3
4x = 6y + 10
let's multiply the first equation by -4 and then add both equations :
-4x = -4y + 12
4x = 6y + 10
--------------------
0 = 2y + 22
2y + 22 = 0
2y = -22
y = -22/2 = -11
x = y - 3 = -11 - 3 = -14
Complete the statement with the correct day. The table shows the amount of time Mrs. Mayes spent word processing each day for four days. Day Time in Hours Monday 5 Tuesday 5 Wednesday 5 Thursday 5 Mrs. Mayes spend the least time working on noselection .
Based on the calculations, Mrs. Mayes spent the least time working on Wednesday.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorIn order to determine when Mrs. Mayes spent the least time working, we would convert the given mixed fractions into a proper fraction and then decimal. Lastly, we would then compare as follows:
Monday = 5 2/5 = 27/5 = 5.4.
Tuesday = 5 5/8 = 45/8 = 5.625.
Wednesday = 5 3/8 = 43/8 = 5.375.
Thursday = 5 4/5 = 29/5 = 5.8.
Based on the calculations above, we can reasonably infer and logically deduce that Mrs. Mayes spent the least time working on Wednesday.
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Complete Question:
The following table shows the amount of time Mrs. Mayes spent word processing each day for four days. On which day did Mrs. Mayes spend the least time working?
Find the area of the figure.
9.8 yd
14.1 yd
Answer:
138.18 square yards
Step-by-step explanation:
Assuming the figure is a rectangle because it isn't said that it is otherwise, you would multiply the numbers together and get 138.18 square yards.
The price on the gas pump is 1/2 the actual price. what is the actually price if the pump registers $6.54
Answer:
$13.08
Step-by-step explanation:
If the price on pump is half the actual price, we just need to double what it says
So
$6.54 x 2 = $13.08
6x+4y-3=0 in standard form
what is the slope of the following line 3x+2y=300
Answer: We have m = −3/2 as the slope and b = 150 as the y-intercept.
Step-by-step explanation:
Given data,
The slope of the following line 3x+2y=300
Define Slope :
Slope = (Change in height)/(Change in width) Or: Slope = rise/run. If y represents the vertical direction on a graph, and x represents the horizontal direction, then this formula becomes: Slope = (Change in y)/(Change in x)
The equation of a line presents the relationship between the components of a line in a certain coordinate system. To construct the equation of the line, we must take note of the parameters such as the slope, a point at which the line passes through, and the intercepts.
We solve for the slope, m, and the y-intercept, b, for the given line. We do this by rewriting the expression into the slope-intercept form,
y = mx + b
We proceed with isolating y in the given equation.
3x + 2y = 300
2y = - 3x + 300
y = (-3x + 300) / 2
y = (-3/2) x + 300/2
y = (-3/2) x + 150
Therefore, we have m = −3/2 as the slope and b = 150 as the y-intercept.
So, slope = -3/2
b = 150
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The range for y=x2+9 is which of the following?
The range of a function y = x² + 9 is y ≥ 9
What is a function?A function is a mathematical expression rule or law that defines the relationship between one variable (dependent variable) and another (independent variable)
What is the range of a function?The range of a function is the set of output values of that function.
What is the range of the given function y = x² + 9?Given the function y = x² + 9, to find the range of the function, we need to find the values of y for which the function is valid.
Making y subject of the formula, we have
x = √(y - 9)
So, the function is valid for √(y - 9) ≥ 0
⇒ y - 9 ≥ 0
⇒ y ≥ 9
So, the range of a function is y ≥ 9
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Which is the graph of the parent function f(x) = |x|?
A.
-10
10
-10
10
The correct option is third graph.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We have the function
f(x)= |x|
The third graph represent the f(x)= |x|.
This is because the absolute value equations grow at a constant rate.
Also, they are absolute so they are also positive.
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The equation (-2) (6x - 5)
The integer solution is
The fraction solution is
Submit Question
0 has two solutions. One is an integer, the other is a fraction.
Answer:
Step-by-step explanation:
Givens
(x - 1)(6x - 5) = 0
Solution
Either one of these can be made into 0 by solving the binomials in the brackets.
x - 2 = 0 Add 2 to both sides
x -2 +2= 0+2 Combine
x = 2
6x - 5 = 0 Add 5
6x -5+5 = 0+5 Combine
6x = 5 Divide by 6
6x/6=5/6
x = 5/6
Answer
Integer Answer: x = 2
Fractional Answer x = 5/6
What did the Nuremberg Laws do:
A. Kept Jews from being German citizens and marked them with a Star of David
B. Establish the policy of mass-murder against the Jews
C. Moved Jews from occupied countries to ghettos
D. Prevented Jews from being teachers or judges
A
Or maybe something else is not sure
Which one of the following probabilities is a cumula tive probability?()
A. The probability that there are exactly 4 pe ople with Type O+ blood in a sample of 10 peopl e.
B. The probability of exactly 3 heads in 6 flips of a coin.
C. The probability that the accumulated annual Yainfall in a certain city next yeay, younded t o the nearest inch, will be 18 inches.
D.The probability that a randomly selected wo man's height is 67 inches or less.
Which one of the following probabilities is a cumula tive probability?()
A. The probability that there are exactly 4 pe ople with Type O+ blood in a sample of 10 peopl e.
B. The probability of exactly 3 heads in 6 flips of a coin.
C. The probability that the accumulated annual Yainfall in a certain city next yeay, younded t o the nearest inch, will be 18 inches.
D.The probability that a randomly selected wo man's height is 67 inches or less
So,the correct option is -
D.The probability that a randomly selected wo man's height is 67 inches or less
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Solve the word problem below using the steps given in the lesson.
Skylar needs $56 to buy a new video game. If he doubles the amount of money he has now, he will have enough to buy
the game with $8 left over.
How much money does Skylar have right now?
PLEASE PLEASE HELP ME!!!!
Answer:
$32
Step-by-step explanation:
56+8=64
64/2=32
The length of a rectangle is four inches smaller than three times its width. Its perimiter is 144 inches. Find the width
The width of the rectangle, w, is: 19 inches.
What is the Perimeter of a Rectangle?The perimeter of a rectangle is the sum of all its four sides which is calculated using the formula:
Perimeter = 2(length + width).
Given:
Perimeter = 144 inches
Width = w inches
Length = 3w - 4 inches
Thus:
2(3w - 4 + w) = 144
2(4w - 4) = 144
8w - 8 = 144
8w = 144 + 8
8w = 152
8w/8 = 152/8
w = 19
Thus, the width of the rectangle, w, is: 19 inches.
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if 125% of a number is 750 what is 65% of the number
Answer:600
Step-by-step explanation:
We have, 125% * x = 750
Multiplying both sides by 100 and dividing both sides by 125
we have x = 750 * 100/125
you then get X=600
Answer:x=600
Step-by-step explanation: Multiplying both sides by 100 and dividing both sides by 125
The length of a rectangle is 3 ft less than double the width, and the area of the rectangle is 44 A?. Find the dimensions of the rectangle.
The dimensions of the rectangle are 8 ft by 5.5 ft.
According to the statement,We have to find that the dimensions of the rectangles.
So, For this purpose, we know that the
A Rectangle may be a four sided-polygon, having all the interior angles adequate 90 degrees.
From the given information:The length of a rectangle is 3 ft but double the width, and therefore the area of the rectangle is 44.
Then
The formula for the world of a rectangle may well be a = L(length) × W(width)A = L × W
Plug in the information:A = 44, L = 2W - 3
b/c but means switch the order before subtracting, W = W
44 = (2W - 3)×W
44 = 2W² - 3W
And then
2W² - 3W - 44 = 0
so,
Factoring: (2W - 11)(W + 4) = 0
2W - 11 = 0 solves to W = 5.5
W + 4 = 0 solves to W = -4
So W = 5.5 and L = 2(5.5) - 3 = 8.
So, The dimensions of the rectangle are 8 ft by 5.5 ft.
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Maia was baking cupcakes for a part.my. She mixed 4 drops of red food coloring for every 6 drops of yellow food coloring to dye her icing orange. circle the ratios of food coloring drops that would create the same orange and justify your choices
Choice 1- 2 red:3 yellow
Choice 2- 24red :26yellow
Choice 3- 40 yellow:100 red
Choice 4- 28 red:42 yellow
Choice 5- 44 red:66yellow
The ratios of the food coloring drops that would create the same orange icing are
Choice 1- 2 red:3 yellowChoice 4- 28 red:42 yellowChoice 5- 44 red:66yellow.What are ratios?Ratios are quantitative measures of how much a variable is contained in another.
Ratios show numerical relationships between quantities.
Ratios are expressed as decimals, fractions, and percentages.
Data and Calculations:The mixture of red coloring = 4 drops
The mixture of yellow coloring = 6 drops
The ratio of red to yellow coloring = 4:6 or 2:3
Choice 1- 2 red:3 yellow = 2:3 (already simplified)
Choice 4- 28 red:42 yellow = 2:3 (when simplified by 14)
Choice 5- 44 red:66yellow = 2:3 (when simplified by 22)
Thus, the ratios of the food coloring drops that would create the same orange icing are Choices 1, 4, and 5.
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