The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
Writing PolynomialsFrom the question, we are to write a polynomial that has a GCF of 7m
That is,
We are to write a polynomial that has a greatest common factor of 7m
Writing the polynomial
14mn - 21m + 49m²n + 7mn²
The polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms
We are to write a polynomial with a GCF of 2ab²
Writing the polynomial
6a²b² - 8ab³ + 4a³b² + 2a³b³
The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms
Hence,
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
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m∠1 =
✔ 131
degrees
m∠2 =
✔ 49
degrees
m∠3 =
✔ 112
degrees
Answer:
what is the question show the pic
Using the standard form of the equation in question 1, what are the length of the radius and the coordinates of the center for this particular circle? Watch your signs for the variables h and k. 12pt
The coordinates of the center is at (1, 0) and the length of the radius is 4 units.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard form of a circle is:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius.
The coordinates of the center is at (1, 0) and the length of the radius is 4 units.
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(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(5x – 3)(
x +
)
Answer:
(4x+5)
Step-by-step explanation:
4x(5x-3)+5(5x-3)
collecting like terms, first part is (5x-3) hence second part of the equation is (4x+5) from the equation above.
Answer:
Step-by-step explanation:
(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(( (5x – 3)(4x +5) ))
A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
Answer:
65.41 u³Step-by-step explanation:
A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.
1/3π2.5²×10 =
1/3π6.25×10 =
1/3π62.5 =
1/3×196.25 =
196.25:3 =
65.41 u³
A $8,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for the year is $405, then how much is invested in each account?
The amount invested in the first account is $1,500 and $6,500 was invested in the second account.
What is simple interest?
Simple interest is determined as the principal multiplied by the interest rate ,then multiplied by the duration of the investment.
The formula for simple interest on an investment is as shown below:
I=PRT
P=principal=$8,000
R=interest rates= 1% and 6%
T=duration of investment=1 year
Let assume that X was invested at 1% and that the remaining of $8000-X is invested at 6%.
Interest on the first account=X*1%*1
Interest on the first account=0.01X
Interest on second account=($8000-X)*6%*1
Interest on second account=480-0.06X
Total interest=0.01X+480-0.06X
Total interest=480-0.05X
Total interest=$405
405=480-0.05X
0.05X=480-405
0.05X=75
X=75/0.05
X=amount invested in the first account=$1,500
Amount invested in the second account=$8000-X
Amount invested in the second account=$8,000-$1,500
Amount invested in the second account=$6,500
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Which of the following tables represents a proportional relationship?
Input
Input Output
7
21
35
49
1357
Input Output
5
42
10
75
15
110
20
145
Input Output
18
46
74
102
26
10
14
Input Output
30
4567
37
44
51
Answer:
The top left answer is correct.
Step-by-step explanation:
If you take each ordered pair and put them in the form y/x. The top left corner is the only one where all of the equations are equivalent.
7/1 = 21/3 = 35/5 = 49/7
What is the answer?im having trouble
Answer:
130
Step-by-step explanation:
let the inside value be,x
x+30°+20°=180°(Being sum of interior angle of triangle)
or,x+50°=180°
or,x=180°-50°
or,x=130°
Now,
let the exterior angle be,a
a=x(VOA)
a=130°
Therefore the value of a is 130°.
Find the surface area of the figure. For calculations involving pi , give both the exact value and an approximation to the nearest hundredth of a unit. Let r=10 and h = 3.
Answer:
exact: SA = 260π in.²
approximate: SA = 816.81 in.²
Step-by-step explanation:
SA = 2πr² + 2πrh
r = 10 in.
h = 3 in.
SA = 2πr(r + h)
SA = 2π(10 in.)(10 in. + 3 in.)
SA = 260π in.²
SA = 816.81 in.²
Two factory plants are making tv panels yesterday plant A produced 3000 panels. Ten percent of the panels from plant A were defective and Three percent from plant B were defective. How many panels did plant be produce if the overall percentage of defective panels from the two plants was 6%. Thanks for the help
Answer: Plant B produced 4000 panels
Step-by-step explanation: Let the number of panels produced by plant A = a and the number of panels produced by plant B = x. In total, we have 3000 + x. Now for the defective panels. 10% of plant a + 3% of plant b = 6% of both a and b. 300 + 3/100(x) = 6/100(3000 + x). 300 + 0.03x = 180 + 0.06x. Now, we simplify. 300 - 180 = 0.06x = 0.03x. So, 120 = 0.03x and 40 = 1% of x. This means x = 4000. So, therefore, Plant B produced 4000 panels. We can check our work by using the value of x we got. 4000 + 3000 = 7000. 6% of 7000 = 420. 120 = 3% of 4000. 120 + 300 = 420 so the answer we got is correct. Hope this helped
Graph this system of inequalities. Identify the solution region on the graph.
y<-x+4, y>-x 2
The system of inequalities y < -x+4 and y >-x 2 do not have a solution
What are inequalities?Inequalities are expressions that have unequal values when compared or evaluated
How to determine the solution to the system?The system of inequalities is given as
y < -x+4
y >-x 2
Next, we plot the inequalities on a graphing tool
See attachment for the graph
From the attached graph, the lines of the inequalities do not intersect
This means that the system of inequalities do not have a solution
Hence, the system of inequalities y < -x+4 and y >-x 2 do not have a solution
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If m = 4 and n = -7, what is the value of m + n?
The answer is -3.
If m = 4 and n = -7, we can evaluate the expression by substitution.
m + n
4 + (-7)
-3
❄ H there,
evaluate this expression by substituting the provided parameters –
[tex]\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}[/tex]
That's it!
❄
Find y'' y = 3 cot x/8
If y = 3 cot x/8, the double differentiation of y gives,
y'' = (3/32) (cosec x/8)(cot x/8)
Given value of y is,
y = 3 cot x/8
Differentiation of the above equation will give us the following,
y' = d(3 cot x/8) / dx
y' = 3d(cot x/8) / dx ........... (1)
Now, we know that the differentiation of cot x is -cosec²x
Therefore, d(cot x/8) / dx = -(cosec²x/8)/8
Thus, equation (1) transforms as follows,
y' = -3(cosec²x/8)/8
Taking differentiation of the above equation, we get,
y'' = -3d((cosec²x/8)/ 8dx
y'' = -6d(cosec x/8) / 8dx [Using chain rule] .......... (2)
As we know, the differentiation of cosec x is -(cosec x)(cot x),
d(cosec x/8) / dx = -(cosec x/8)(cot x/8) / 8 [Using chain rule]
Therefore, equation (2) can be written as,
y'' = -(-6(cosec x/8)(cot x/8) / (8×8)
∴ y '' = 3(cosec x/8)(cot x/8) / 32
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Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answer:
c = 2.25
Step-by-step explanation:
The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.
SolutionWe can find -c from ...
P(x < -c) = (1 - 0.9756)/2 . . . . . the area in the lower tail
The calculator tells us -c = -2.25.
c = 2.25
Each outcome or a collections of outcomes in a experiment is called as?
Answer:
event
What is an event?
An event can be described as an individual or set of outcomes of an experiment.
Events are a subset of the experiment's sample space.
What is sample space?The sample space of an experiment is the complete set of possible outcomes of that experiment.
Please help it would be much appreciated
Answer:
calcium =1x40=40
chlorine=2x35=70
40+70=110
ca=40/110×100=36.36
when we approximate it become 36.4
thanks
Poormina spends all of her money on comic books and mandarins. in 2013, she earn $12 per hour, the price of a comic book was six dollars, and the price of a mansion was one dollar
The price of a mansion is $1.00 in 2013.
What is difference between a nominal and real variable?
Nominal variables are expressed in money or dollar terms, whereas the real variable compares the wage earned per hour to the basket of goods or services that it can purchase.
In comparing the wage earned per hour to 2 comic books, since the two would cost $12,that explains real variable, which is not required in this case.
However, comparing the the wage of $12 per hour to the price of mansion, which is $1 per one, indicates nominal variable.
In essence, the correct option in this case is that price of a mansion is $1.00 in the year 2013.
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Income Statements under Absorption Costing and Variable Costing
The demand for aloe vera hand lotion, one of numerous products manufactured by Smooth Skin Care Products Inc., has dropped sharply because of recent competition from a similar product. The company's chemists are currently completing tests of various new formulas, and it is anticipated that the manufacture of a superior product can be started on December 1, one month in the future. No changes will be needed in the present production facilities to manufacture the new product because only the mixture of the various materials will be changed.
The controller has been asked by the president of the company for advice on whether to continue production during November or to suspend the manufacture of aloe vera hand lotion until December 1. The controller has assembled the following pertinent data:
Smooth Skin Care Products Inc.
Income Statement—Aloe Vera Hand Lotion
For the Month Ended October 31
Sales (400,000 units) $32,000,000
Cost of goods sold 28,330,000
Gross profit $3,670,000
Selling and administrative expenses 4,270,000
Loss from operations $(600,000)
The production costs and selling and administrative expenses, based on production of 400,000 units in October, are as follows:
Direct materials $15 per unit
Direct labor 17 per unit
Variable manufacturing cost 35 per unit
Variable selling and administrative expenses 10 per unit
Fixed manufacturing cost $1,530,000 for October
Fixed selling and administrative expenses 270,000 for October
Sales for November are expected to drop about 20% below those of the preceding month. No significant changes are anticipated in the fixed costs or variable costs per unit. No extra costs will be incurred in discontinuing operations in the portion of the plant associated with aloe vera hand lotion. The inventory of aloe vera hand lotion at the beginning and end of November is expected to be inconsequential.
Required:
Question Content Area
1. Prepare an estimated income statement in absorption costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Absorption Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
Sales
$Sales
32,000,000
Cost of goods sold:
Direct materials
$Direct materials
Direct labor
Direct labor
- Select -
- Select -
- Select -
$- Select -
Selling and administrative expenses:
$- Select -
- Select -
blank
blank - Select -
$- Select -
Question Content Area
2. Prepare an estimated income statement in variable costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Variable Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
$- Select -
Variable cost of goods sold:
$- Select -
- Select -
- Select -
blank
blank - Select -
$- Select -
- Select -
$- Select -
Fixed costs:
$- Select -
- Select -
blank
blank - Select -
$- Select -
The estimated income statement for the month shows a loss of $840000.
How to illustrate the income statement?The estimated income statement for the month will be:
Sales = $25,600,000
Less: Cost of goods sold
Direct materials (320000 × 15) = $4,800,000
Direct labor (320000 × 17) = $5,440,000
Variable costing (320000 × 15) = $11,200,000
Fixed manufacturing cost = $1,530,000
Total cost of goods sold = $22970000
Gross profit = $25,600,000 - $22970000 = $2,630,000
Gross profit = $2,630,000
Less:
Variable selling and administrative expense = $3200000
Fixed selling and administrative = $270000
Loss from operations = $840000
Therefore, the estimated income statement for the month shows a loss of $840000.
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For a segment of a radio show, a disc jockey can play 7 records. If there are 13 records to select from, in how many ways can the program for this segment be arranged?
The number of ways the program can be arranged for this segment is 8, 648, 640 ways
What is permutation?It is important to note that the formula for finding the permutation or arrangement of a set of dats is given as;
Permutation = [tex]\frac{n!}{(n-r)!}[/tex]
where
n = number to select from = 13r = number of objects selected = 7Let's substitute the values into the formula for permutation, we have
Permutation = [tex]\frac{13!}{13 - 7!}[/tex]
Find the difference of the denominator
Permutation = [tex]\frac{13!}{6!}[/tex]
Find the factorial of the values
Permutation = [tex]\frac{6,227,020,800}{720}[/tex]
Divide the numerator by the denominator
Permutation = 8, 648, 640 ways
Thus, the number of ways the program can be arranged for this segment is 8, 648, 640 ways
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A stamp collection consisting of 23 stamps includes 4¢ stamps and 9¢ stamps. The total value of the stamps is $1.27. Find the number of each type of stamp in the collection.
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. Thus the required number of stamps are:
4¢ stamps = 16
5¢ stamps = 7
A simultaneous equation is a set of equations that has to be solved in relation to each other at the same time. This process is required so as to determine the values of two unknowns e.g x and y.
From the given question, let the number of 4¢ stamps be represented by n, and that of the 9¢ stamp be represented by m.
So that,
n + m = 23 ............ 1
But 100¢ = $1, so that;
4¢ = x
x = [tex]\frac{4}{100}[/tex]
= $0.04
also,
9¢ = x
x = [tex]\frac{9}{100}[/tex]
= $0.09
Thus, we have;
0.04n + 0.09m = 1.27 ......... 2
From equation 1, make n the subject of the formula, such that;
n = 23 - m ........... 3
Substitute equation 3 into equation 2
0.04(23 - m) + 0.09m = 1.27
0.92 - 0.04m + 0.09m = 1.27
collect like terms to have;
0.05m = 1.27 - 0.92
= 0.35
m = [tex]\frac{0.35}{0.05}[/tex]
m = 7
Now substitute the value of m into equation 3
n = 23 - m ........... 3
= 23 - 7
n = 16
Therefore the number of 4¢ stamps is 16, while that of the 5¢ stamps is 7.
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What is the measure of RCP?
Answer:
84
Step-by-step explanation:
15+15+27+27
What is the length of each leg of the triangle below?
Answer:
C
Step-by-step explanation:
32/sqrt(2) = 32sqrt(2)/2 = 16sqrt2
Answer:
C.
Step-by-step explanation:
It is a right triangle with hypotenuse c = 12, also for having two equal angles is an isosceles triangle, the missing sides (catethus) are equal (a and b)
a = b = the legs
Apply the Pythagorean theorem
[tex]c^{2}=a^{2} +b^{2} \\c^{2} =2a^{2}[/tex]
[tex]a^{2} =\frac{c^{2} }{2}=\frac{(32)^{2} }{2} =512[/tex]
[tex]a=\sqrt{512} =\sqrt{256(2)} =16\sqrt{2}[/tex]
Hope this helps
anna bought a sweater at 40% off the original price. if she paid $12 what was the original price of the sweater?
Answer:
The original price was $30
Step-by-step explanation:
40% = 40/100 = 0.4
[tex]\frac{12}{0.4} =30[/tex]
Hope this helps
What are the leading coefficient and degree of the polynomial?
2+18u^4+9u-u^8
Leading coefficient:
Degree:
Answer:
-1 and degree 8
Step-by-step explanation:
the highest degree carry the leading coefficient, and the highest power take the highest degree
One hundred dollars less
than twice last year's
income?
Answer:
2y - 100
Step-by-step explanation:
Last year's income = y
2y-100
When an integer is subtracted from 2 times the next consecutive odd integer, the difference is 1. Find the value of the greater integer.
The value of the greater integer which is the next consecutive odd integer is; -1.
What is the value of the greater integer as described by the task content?By observation, it follows that the first integer can be represented by 2x+1 while the next consecutive odd integer can be represented as 2x+3.
Hence, it follows that we have;
2(2x+3) - 2x - 1 = 1
4x +6 -2x - 1 = 1
2x = -4
x = -2.
Consequently, the value of the next consecutive greater integer is; 2(-2) + 3= -1.
It consequently follows from the computations above that the value of the greater odd integer is; -1.
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Create a linear equation based on an experience in your everyday life. In this experience, a variable should depend on at least one other variable (the independent variable(s)). If your equation has 2 variables, graph it on the coordinate plane.
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let y represent the total salary earned by working x hours, hence, if I earn $10 per hour:
y = 10x
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
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Which shapes have less than 3 lines of symmetry?
A) B and C
B) A and D
C) B and D
D) A and C
The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
How to determine the shapes that have less than 3 lines of symmetry?The shapes are given as:
Isosceles trapezoidSquareIsosceles triangleRegular PentagonThe lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same
As a general rule:
An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry
Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
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What is the mean of 13, 7, 8 and 4
Answer:
16
Step-by-step explanation:
Mean is same as average. To find the average, add all items and divide the sum by the number of items in the list.
Avg = (13 + 7 + 8 + 4) / 2 = 32 / 2 = 16
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
To find the mean you first need to add all numbers and divide by how many there are :
[tex]\sf{\dfrac{13+7+8+4}{4}}[/tex]
⨠ simplify
[tex]\sf{\dfrac{32}{4}}[/tex]
[tex]\boxed{\sf 8}[/tex] [tex]\tiny\pmb{\sf{Frozen \ melody}}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
If the scale factor between two circles is 2x/5y, what is the ratio of their areas?
Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
What is the area ratio of two circles?According to the statement we know that the radius ratio between two circles. Given that the area of the circle is directly proportional to the square of its radius, then the area ratio is shown below:
A ∝ r²
A = k · r²
A' · r² = A · r'²
A' / A = r'² / r²
A' / A = (r' / r)²
A' / A = [(2 · x) / (5 · y)]²
A' / A = (4 · x²) / (25 · y²)
Given that the length ratio between the radii of the two circles is (2 · x) / (5 · y). The ratio of the areas of the two circles is (4 · x²) / (25 · y²).
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At Indianapolis Motor Speedway, one lap is 2.5 miles in length. The average speed of an Indy racing car is 190 miles per hour.
15. Find the length of one lap in yards.
16. How many seconds would it take to complete one lap?
Answer:
15. 4400 yards
16. 47.4 seconds
Step-by-step explanation:
15. 1 mile = 1760 yards
2.5 miles:
2.5(1760) = 4400 yards
16. t = 2.5/190 = 0.013150 h
1 hour = (60)(60) = 3600 seconds
Then 1 lap take
=(0.013150)(3600) = 47.4 seconds
Hope this helps