A rectangle measuring 8 inches by 6 inches needs squares of side. A function in an in which the box's volume is 4a³-28a²+48a.
Given that,
A square measuring 8 inches by 6 inches needs squares of side. A cut out of each corner so that the sides can be folded into a box without a top.
How much area a box can occupy is determined by its volume. You need to know a box's length, width, and height in order to compute its volume. By multiplying the base area by the box's height, one can get the volume of a box.
The measurement of how much space an object may occupy is called volume, which is also known as capacity. Both regular and irregular objects may be present. Cubes, blocks, cylinders, pyramids, cones, and spheres are examples of common objects.
A: area of the base
L: Length of the base
W: Width of the base
V(a)= (8-2a) (6-2a) (a)
V(a)= (48-16a-12a+4a²) (a)
V(a)= (48-28a+4a²) (a)
V(a)= 48a-28a²+4a³
V(a)=4a³-28a²+48a
Therefore, a function in an in which the box's volume is 4a³-28a²+48a.
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I was seeing if anybody can solve this question
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 5}(x-\stackrel{x_1}{0})\implies y=5x+8[/tex]
Raj bought six 3-litre cans of sunflower oil.
He poured all the sunflower oil equally into 20 bottles.
What was the volume of sunflower oil in each bottle?
Answer:
0.9 Litres or 900 ml
Step-by-step explanation:
First we will find out the total volume of Sunflower oil he has.
Sunflower Oil bought = 6 cana x 3 litre = 18 litres
Now we divide this 18 litres into 20 parts to find out the volume of sunflower oil per bottle:
[tex] \frac{18}{20} \\ = \frac{9}{10} \\ = 0.9litres \: or \: 900ml[/tex]
A bookstore sells a textbook for $35.10. If the bookstore makes a profit of 30% on each sale, what does the bookstore pay the publisher for each book?
The bookstore pays the publisher $27 for each book thus making a profit of 30%.
The profit is defined as the difference between the sell price and the cost price.
The sell price is defined as the price at which an object is sold.
The cost price is defined as the price at which an object is bought.
When the sell price is greater than the cost price profit is made by the seller.
Let the cost price (price paid to publisher) be x dollars.
Therefore when sold at a profit of 30% then
profit= 30%of x=0.3x dollars
Now the sell price = cost price +profit
∴Sell price= x+0.3x=1.3x
But the sell price is given as $35.10
So we can equate the two terms to get a linear equation in x.
∴1.3x=35.10
or, x=35.10÷1.3
or, x=27
Therefore the cost price is $27.
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Maria works for a salary of $2,750 per month. She has federal income tax withheld at the rate of 15 percent, Social Security tax withheld at the rate of 7.2 percent, Medicare tax withheld at the rate of 1.37 percent, and health insurance premiums of $76 per month. Maria’s net pay is $____________.
Maria’s net pay is $2,025.82.
What is the net pay?The net pay is the gross pay minus mandatory and voluntary deductions, like taxes, insurance, and other expenses.
The net pay represents the amount of money the income earner receives.
The net pay is also known as the take-home.
Data and Calculations:Monthly salary = $2,750
FICA withholding = 15%
Social security tax withholding = 7.2%
Medicate tax withholding = 1.37%
Health Insurance Premium = $76 per month
Total withholding = 23.57%
= $648.18 (2,750 x 23.57%)
Total deductions and withholding = $724.18 ($76 + $648.18)
Net pay = $2,025.82 ($2,750 - $724.18)
Thus, Maria's net pay after the withholdings and deductions is $2,025.82.
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find the equation of line that goes through (-1, -2) and parallel to y = 9x + 4
Answer:
y = 9x + 7
Step-by-step explanation:
Line is parallel to y = 9x + 4 and passes through the point (-1, -2)
m = slope
the slope of the line is the same for both lines, m = 9
the equation of the parallel line is y = 9x + a
-2 = (9) * (-1) + a
a = 7
y = 9x + 7
The perimeter of a square must be greater than 102
102
inches but less than 112
112
inches. Find the range of possible side lengths that satisfy these conditions.
The possible range for side lengths of the square is (25.25 to 28) both values not included.
What is defined as the square?A square is made up of four sides and four vertices. A square's sides are all the same length. The perimeter of the a square would be the total length of each of its sides. As a result, we can calculate the perimeter of such a square by adding its four sides. The given square's perimeter is a + a + a + a. We just need one side of a square to obtain its perimeter because all of its sides are equal.For the given question;
Let the side length of the square be 'a'.
The, the perimeter of the square is 4a.
The perimeter must be less than 112.
Thus, 4a < 112.
The perimeter also must be greater than the 102.
4a > 102.
So, the combined inequality will be.
102 < 4a < 112
Divide the inequality by 4
25.25 < a < 28.
Thus, the side length of the square must be greater than 25.25 inches and less than 28.
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The diagram below represents the rate of making copies on a copy machine. Which table represents this rate? Copies : 15 Seconds : 5
Answer:
The answer would be A.
Step-by-step explanation:
You can eliminate b because 15/5=3 copies but 5/5 would be 1 not 15. You can eliminate d because 15/3=5 copies but 5/3 would not equal 1. You can eliminate c because 15/15=1 but 5/15 does not equal 3.
Enter an equality that represents the graph in the box. Please help me!
Answer:
y [tex]\geq[/tex] 4x - 6
Step-by-step explanation:
1. Find the slope using the slope formula (rise over run)
2. Use the slope and one of the points to solve for the y-intercept (b)
3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line
6. Sal is selling two types of printed socks. He sells type a at R45 a pair. He sells type b at R30. If he sold 16 pairs in total, and had a total income of R585, how many pairs of sock b did Sal sell?
Step-by-step explanation:
a + b = 16
a = 16 - b
45a + 30b = 585 | divide both sides by 15
3a + 2b = 39
now we are using the first in the second equation :
3(16 - b) + 2b = 39
48 - 3b + 2b = 39
48 - b = 39
48 = 39 + b
9 = b
he sold 9 pairs of type b socks.
FYI :
a = 16 - b = 16 - 9 = 7
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PLEASE HELP!!!!! Under a dilation centered at the origin, the vertex, (3, −5), of a polygon is moved to the point (−15, 25) .
What is the scale factor of the dilation?
Enter your answer in simplified form in the box.
The scale factor of the dilation is -5
What is the scale factor of the dilation?The points are given as
Point = (3, -5)
Image = (-15, 25)
The scale factor of the dilation is calculated using
Scale = Image/Point
So, we have
Scale = (-15, 25)/(3, -5)
Evaluate
Scale = -5
Hence, the scale factor of the dilation is -5
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Assume that the situation can be expressed as a linear cost function. Find the cost function in this case.
Marginal cost: $15; 150 items cost $5500 to produce.
The linear cost function is C(x) =
The linear cost function is C(x) = 15x + 3250 and the cost function in marginal cost: $15; 150 items cost $5500 to produce is $ 5500 .
The linear operate is expressed as y = mx + b .....(1)A linear value operate expresses value as a linear operate of the amount of items;Let C(x) is that the total value, and x is that the range of things.
The slope "m" is named the cost and "b" is named the charge.
The value of m is $15 and the price of "x" is 150.
Total cost of 150 items are $5500
Substitute all the values within the equation (1) , we get
5500 = 15 (150) + b
5500 = 2250 + b
3250 = b
Hence , linear cost function is given by C(x) = 15x + 3250
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Find n(A) for the set A
Answer:
This is the answer for the sequence
If f(x) = square root of x, which equation describes the graphed function
The equation that describes the graphed function is [y = f(-x + 4)].
As per the question statement, we are provided with the information about a function f(x) which is equal to square root of "x", and a reference graph diagram.
We are supposed to determine the equation from the given four options that describes the graphed function.
To solve this question, we will use the trial and error method, using the options to determine out correct answer.
First of all, from the graph, we can see that the graph cuts the x-axis at
(4, 0) and y-axis at (0, 2). Now, since [y = f(x)], our equation must be equal to 0 when (x = 4) is substituted, and 2 when (x = 0).
Considering option (A), [tex]y=f[(-x)+4]=\sqrt{[(-x)+4]}[/tex], and substituting
(x = 4), we get,
[tex]y=\sqrt{[(-4)+4]}\\or, y=\sqrt{(4-4)}\\ or,y=\sqrt{0}\\ or,y=0[/tex]
While substituting (x = 0), we get,
[tex]y=\sqrt{[(-0)+4]}\\or, y=\sqrt{(4-0)}\\ or,y=\sqrt{4}\\ or,y=2[/tex]
Hence, option (A) satisfies at the points of (4, 0) and (0, 2).
Similarly, if we substitute and check on the other three options, we will see that for (x = 4), (y ≠ 0) and for (x = 0), (y ≠ 2).
Therefore, if [f(x) = (√x)], then the equation that describes the graphed function is [y = f(-x + 4)].
Function: In mathematics, a function is an operator which when provided with an input, will perform a specified set of operations on the input and then produce a specified output.To learn more about Functions, click on the link below.
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Write a short essay of the given topic "The Fibonacci sequence and its uses in understanding real-life problems".( I need answer ASAP)
Answer:
The Fibonacci sequence is a series of numbers in which each number is the sum of the two that precede it. Starting at 0 and 1, the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on forever. The Fibonacci sequence can be described using a mathematical equation: Xn+2= Xn+1 + Xn.
Step-by-step explanation:
What is the area of?
6- sqaureroot 11 and 6+ sqaureroot 11
an accountant needs to withhold 21% of income for taxes if the income is below $40,000 and 26% of income if the income is $40,000 or more. The income amount is in cell A1 Write a spreadsheet expression that would calculate the amount withhold.
A spreadsheet expression=IF(A1<40000,(21%*I21),(26%*A1))
The "IF" function should be used in the spreadsheet expression. The "IF" function returns a value based on the criteria specified in the spreadsheet formula. This, like other spreadsheet functions, begins with =.In response to the question,
Cell A1 contains the value to be inspected. If A1 is smaller than $40000 (written as A140000), the spreadsheet performs the following function: (21%*I21). otherwise (which may be understood as A1 higher than or equal to $40000 in this example), calculate the following command as indicated above; (26%*A1).
The command is finished with the last parenthesis.
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someone pls help me FAST
maysa made an error in her work on the folowing problem
3.5 - 2.46 = 1.16
describe maysa's error. explain how you would use a model or place-value concepts to help maysa build understanding
pls help fast will give brainliest if i like the answer!!
Answer:
Maysa forgot to subtract from the hundredths place
3.5= 3.50
3.50
-2.46
1. 04
a) A couple of entrepreneurial business students decided to put their education into practice by developing a tutoring company for business students. While private tutoring was offered, it was determined that group tutoring before tests in the large statistics classes would be most beneficial. The students rented a room next to campus for P3000.00 for 3 hours. They developed handouts based on past tests and these handouts (including colour graphs) cost P50 each. The tutor was paid P250 per hour for a total of P750 for each tutoring session.
i) If students are charged P200 to attend the session, how many students must enrol for the company to break evenA somewhat smaller room is available for P200 for 3 hrs. The company is considering this possibility. How would this affect the BEP?
According to the information, it can be inferred that in the room worth 3,000, the break-even point would be 25 students enrolled. On the other hand, in the room of 200, the break-even point would be 7 students enrolled.
What is the Break-even point?The break-even point is an economic term to refer to the moment when a company's income covers its fixed and variable expenses, that is, when you manage to sell the same amount you spend, you neither win nor lose, you have reached the break-even point.
Thus, calculating the break-even point is essential for companies to assess their profitability, since in this way it is possible to know how much they need to sell to generate profit. Knowing this value, even before starting a new project, allows you to know how financially interesting your business idea is.
How to clculate the break-even point in this case?To calculate the break-even point, we must take into account the expenses that the students will have to offer their service:
Room 1: 3,000Room 2: 200Tutor: 750According to the above, the expenses in case A, with room 1 would be:
3,000 + 750 = 3,750On the other hand, the expenses in case B with room 2 would be:
200 + 750 = 950So, we know that in case A the expenses are going to be 3,750 and in case B the expenses are going to be 950. To find the break-even point for each case, we must divide this value by the price at which they are going to sell the item. course to students. However, it should be clarified that it must be divided by 150 because 50 will be used to pay for each student's handouts.
3,750 ÷ 150 = 25
950 ÷ 150 = 6.33 = 7
According to the above, the break-even point for case A would be 25 students. Additionally, in case B the balance point would be 6.33 students who are close to 7.
To conclude, it can be stated that the best option would be to take room 2 because they will have fewer expenses and will have to sell fewer units of their course to reach the break-even point.
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y=5x−3
Find the output, yyy, when the input, xxx, is 555.
y = 5x-3
The solution of an equation refers to the values of the variables involved in that given equation. The value of output y is 22.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
The Solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.
For a solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point
The expression is y = 5x-3
We need to determine the output y, when the value of input is x is 5 so
That is, substituting in , we get the following;
y = 5x-3
y = 5(5)-3
Multiplying the value within the bracket, we have;
y = 25-3
Then Subtracting the terms, we get,
y = 22
Therefore, the value of output y is 22.
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The complete question is
Find the output, y, when the input, x, is 5. The equation is y = 5x-3
help me with this please in need it now
The price of of 1 pound of almond is given as 2.2/0.65
Unit rate of change of a lineA line is defined as the shortest distance between two points. Given the coordinate (0.65, 2.2)
This shows that 0.65 pound of almond costs $2.2. For the cost of one pounds of almond;
Unit price = 2.2/0.65
Unit price = $3.38
This shows that the price of of 1 pound of almond is given as 2.2/0.65
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The product of 9 and Jenny's age is 135
The product of 9 and Jenny's age 15 is 135.
What is a mathematical operation?Similar to the principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action of the operation on each function.So, let the missing value be 'x'.
Then,
9 × x = 1359x = 135x = 135/9x = 15Therefore, the product of 9 and 15 is 135.
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What is the smallest even whole number which is divisible by 3
Answer:
the smallest even whole number which is divided by 3 is 6
The following are the transactions of Spotlighter, Incorporated, for the month of January. Borrowed $4,790 from a local bank on a note due in six months. Received $5,480 cash from investors and issued common stock to them. Purchased $2,700 in equipment, paying $1,050 cash and promising the rest on a note due in one year. Paid $1,150 cash for supplies. Bought and received $1,550 of supplies on account. Required: Post the effects to the appropriate T-accounts and determine ending account balances. Show a beginning balance of zero.
The final balance in the account is $9,620
How to get the final balance of Spotlighter, Incorporated.?
Here we need to write an addition. The amounts that the company receive will be positive amounts, while the amount that the company pays will be represented by negative amounts, then:
Borrowed $4,790 from a local bank: +$4,790 Received $5,480 cash from investors: + $5,480 Purchased $2,700 in equipment (only pays $1,050 of this): - $1,050 Paid $1,150 cash for supplies: -$1,150 Bought and received $1,550 of supplies on account: + $1,550Now we can add these values, assuming that the initial balance is $0.
$0 + $4,790 + $5,480 - $1,050 - $1,150+ $1,550 = $9,620
This is the balance, they still have a debt of $4,790 and $1,650, but the amount of money that they have in the account is $9,620
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Question 6
Find m/IJP if mZIJP = x + 117,
m/IJK 150°, and m/PJK = x + 47.
If the linear equation [(x + 117) = 150°], then the value of (x + 47) will be 80.
As per question statement, we are provided with a linear equation, as
[(x + 117) = 150°].
We are required to calculate the value of (x + 47) using the above mentioned equation.
To solve this question, we will find out the value of "x" from the equation
[(x + 117) = 150°] and then, add 47 to the value of x to obtain our desired answer, i.e.,
[tex][(x + 117) = 150]\\or, x=(150-117)\\or,x=33\\or, (x + 47)=(33+47)\\or, (x + 47)=80[/tex]
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A naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet then 145 is the position of the submarine relative to the surface of the ocean now.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
If a naval submarine was operating 310 feet below the surface of the ocean. To pass above an underwater mountain, or seamount, it rose 165 feet. we need to find the position of the submarine relative to the surface of the ocean now.
The submarine initial position= 310 feet.
To pass above an underwater mountain, or seamount, it rose = 165 feet.
The position of submarine is
310-165
=145 feet.
Therefore the position of the submarine relative to the surface of the ocean now is 145 feet.
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BX bisects ABC to form two congruent acute angles. What type of angle can ABC be? Select all that apply
O Acute
O Right
Obtuse
Straight
The types of angle can ABC be are (a) Acute (b) Right and (c) Obtuse
How to determine the angle types?The statement is given as:
BX bisects ABC to form two congruent acute angles
The above statement means that the smallest type of angle, the angle ABC can be is an acute angle
Also, when a right angle is divided into 2 (or bisected), the resulting angles are acute angles.
Lastly, when an obtuse angle is bisected, the resulting angles are acute angles.
Hence, the types of angle can ABC be are (a) Acute (b) Right and (c) Obtuse
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Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the tickets.
I really need help please
Answer:
see attached
Step-by-step explanation:
Given a partially-filled circle pattern, you want to place the remaining numbers so the sum in each circle is 21.
ApproachThere are seven (7) circles, and nine (9) unknown values. This means there are a couple of "free choice" values that cannot be found directly. Our approach is to limit the number of possibilities we must examine.
EquationsWe note that if we multiply the sum (21) by the number of circles, that product includes the "single cover" circle shapes once, and each of the overlapping "double cover" areas twice. There are three unknown "single cover" values, and six unknown "double cover" values. If we represent the sums of these by "s" and "d" respectively then we have ...
(10 +11 +6 +4 +s) +2(d +5) = 7×21
41 +d +2s = 147 . . . simplify
d +2s = 106 . . . . . . subtract 41
The total of all of the unplaced numbers is ...
(2 +12 +7 +14 +1 +8 +9 +3 +13) = s +d
69 = s +d
Now, we have two equations in s and d:
d +2s = 106d +s = 69Subtracting the second from the first gives ...
(d +2s) -(d +s) = (106) -(69)
s = 32
The sum s is the sum of 'a', 'b', and 'c' as marked in the attachment. There is only one set of unplaced numbers that has a total of 32: {7, 12, 13}.
Using these numbers means that the set of allowed values for the "double cover" areas is {1, 2, 3, 8, 9, 14}.
Trial and errorWorking clockwise from the space marked 'c' in the attachment, the "double cover" oblong spaces must have the values ...
16 -cc -515 -c6 -(a -c)9 +(a -c)8 -(a -c)As we noted above, {a, b, c} is some permutation of {7, 12, 13}. This means the value (a-c) will be one of ±1, ±5, ±6.
If (a-c) = ±6, then 6 -(a-c) = {0, 12}. Neither value is allowed: 0 is not on the list, and 12 is already used.
If (a-c) = ±5, then we would have ...
for (a-c) = -5, 6 -(a-c) = 11, not an allowed value (already used).
for (a-c) = 5, all of the values 6-5=1, 9+5=14, and 8-5=3 are allowed. This case corresponds to {a, b, c} = {12, 13, 7}.
If (a-c) = ±1, then we would have 6 -(±1) = {5, 7}. Neither value is allowed.
ConclusionThe only allowed choice for {a, b. c} is {12, 13, 7}. Using c=7 and (a-c)=5, the "double cover" values clockwise from 'c' are ...
16-7 = 97 -5 = 215 -7 = 86 -5 = 19 +5 = 148 -5 = 3When all of the values are filled in the diagram it looks like the attachment.
__
Additional comment
As you might imagine, there was a bit of thrashing around before this method of solution presented itself. The system of 7 equations in 9 unknowns cannot be solved directly, and we know of no way to include the requirement that the solution set must include each number of the given set, used only once.
Fortunately, the method we tried here proved to find a solution in fairly straightforward fashion.
If a 2-liter bottle holds 67 3/5 ounces, about how many 8-ounce cans will it take to fill the 2-liter bottle?
A. 13
B. 22
C. 8
D. 4
By taking the quotient between the two volumes in ounces, we conclude that you will need about 8 cans to fill the bottle. So the correct option is C.
How many 8-ounce cans will take to fill the 2-liter bottle?We know that the 2-liter bottle holds (67 + 3/5) ounces of water, and each one of the cans holds a volume of 8 ounces.
To see how many cans we need to fill the bottle, we need to take the quotient between the two volumes (using ounces in both cases, obviously), we will get:
Q = (67 + 3/5)/8 = 8.45
So you need 8.45 cans to completely fill the 2 liter bottle, then we can see that the correct option will be C, 8 cans, as that is the best estimation.
We conclude that you need about 8 cans to fill the bottle.
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