The combination should be 20 of Brand A and 20 of Brand B.
What is Linear Programming?When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
Given:
Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.
Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.
So, Max Z = 400x + 600 y
Constraints:
100x + 200 y ≤ 6000
or, 400x + 200y ≤ 12000
Solving the Equation:
300x = 6000
x= 20
and, y= 20
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Given the function: calculate the following values.
The values of f(-1) , f(0) and f(2) are 0, 8 , 16 .
What is a function ?
Function can be defined in which it relates an input to output.
Given function ,
f ( x ) = 4x + 4 when x < 0
= 4x + 8 when x >= 0
f(-1) = 4x + 4
= 4 ( -1 ) + 4
= 0
f(0) = 4x + 8
= 4*0 + 8
= 8
f(2) = 4x + 8
= 4*2 + 8
= 8 + 8
= 16
Therefore, The value of f(-1) , f(0) and f(2) are 0, 8 , 16 .
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Find dy/dx by implicit different iation xy^2= 4.
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
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Two draws are made at random without replacement from a box containing the following five tickets:
1 2 3 4 3
What is the probability that the sum of the tickets is 5?
in %
The probability that the sum of the ticket is 5, expressed as a percentage is 30%
What is the probability that an event will occur?The probability that an event will occur can be found by the ratio of the number of times the event occurs to the number of all possible events.
The five tickets in the box = 1, 2, 3, 4, 3
The tickets that sum to 5 are; 1 and 4, 2 and 3
The probability that the first ticket picked is 1 = 1/5
The probability that the next ticket picked is a 4 = 1/(5-1) = 1/4
Therefore, the probability of picking a 1 and 4 = (1/5) × (1/4) = 1/20
Similarly, the probability of picking a 4 and then a 1 is 1/20
The probability of picking tickets with numbers 1 and 4 in either order therefore = 2 × 1/20 = 1/10
The probability that the first ticket drawn is 2 = 1/5
The probability that the next ticket picked is a 3 = 2/(5-1) = 1/2
Therefore, the probability to draw a 2 and 3 = (1/5) × (1/2) = 1/10
The probability that the first ticket picked is 3 = 2/5
The probability that the next ticket picked is a 2 = 1/(5-1) = 1/4
Therefore, the probability of picking a 3 and 2 = (2/5) × (1/4) = 2/20 = 1/10
The probability of picking a 2 and a 3 in either order is therefore;
1/10 + 1/10 = 2/10 = 1/5
The probability that the sum of the ticket is 5, is the sum of the probabilities of picking a 1 and a 4 and the probability of picking a 2 and a 3, which is; 1/10 + 1/5 = 3/10 = 0.3
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Marsha deposited $7,000 into a savings account 4 years ago. The simple interest rate is 2%. How much money did Marsha eam in interest?
Answer:
$560
Step-by-step explanation:
The formula for simple interest is:
I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).
Plugging in the values, we get:
I = $7,000 * 2% * 4 years = $560
So, Marsha earned $560 in interest.
In the diagram below, AD EB, m/ABD = 115° and m/D = 27°.
Find m < ABE
The value of angle ABE is 52°
What are interior angle of a triangle ?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.
The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.
The sum of interior angle in a triangle is 180°
Angle EBD = 180-(90+27)
= 180-117
= 63°
angle ABE + EBD = ABD
ABE = ABD - EBD
ABE = 115-63
= 52°
Therefore the value of angle ABE is 52°
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Everyone should have free Internet access to education, news, jobs, and more.
The graph plots education and news on the x-axis and other goods and services on the y-axis.
Draw the economy's PPF before the Internet and label it PPF0.
Draw the PPF after the arrival of the Internet if the effect on education and news is greater than on other goods and services. Label it PPF1.
From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.
What is graphs?Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.
Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.
Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.
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-5-
5
3
24
or to w
4
(0)4
23 45 X
900
Which function represents g(x), a reflection of f(x) = //
(10)* across the x-axis?
O g(x) = -(10)*
Og(x) = -
O g(x) =
5 10
10
g(x) = (10)*
The reflected function across the {x} - axis would be -
g(x) = -2/5 (10)ˣ.
What is the resultant function when f(x) is reflected across the {x} - axis?If the function f(x) is reflected across the {x} - axis, then the new function g(x) becomes -
g(x) = - f(x)
Given is the function as -
f(x) = 2/5 (10)ˣ
We can write the reflected function as -
g(x) = - f(x)
g(x) = - {2/5 (10)ˣ}
g(x) = -2/5 (10)ˣ
Therefore, the reflected function across the {x} - axis would be -
g(x) = -2/5 (10)ˣ.
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Select the independent pair(s) of events.
=break your pencil lead while writing, and = feel overly stressed.
=put together a swing set correctly, and =read the directions.
=make an error on your income tax return, and =file Form 1040 long.
=have a salad with dinner, and =work on a home project.
STATS 2332
=break your pencil lead while writing, and = feel overly stressed.
=put together a swing set correctly, and =read the directions.
These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).
=make an error on your income tax return, and =file Form 1040 long.
These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.
=have a salad with dinner, and =work on a home project.
These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.
What is the quotient and remainder, written as partial fractions, of
15x²+52x +43
3x²+5x-8
The quotient and remainder, written as partial fractions, of 15x²+52x+43/3x²+5x-8 would be A/(3x + 8) + B/(x - 1) where A is -8/3 and B is 1.
What in mathematics is a partial fraction?
The fractions that are utilized to break down a rational expression are called partial fractions.
Any component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.
15x²+ 52x + 43/3x²+5x-8
15x²+52x +43/3x² + ( 8 -3)x - 8
15x²+52x +43/3x² + 8x -3x - 8
15x²+52x +43/3x(x - 1) +8(x - 1 )
15x²+52x +43/(3x + 8)(x -1 )
A/(3x + 8) + B/(x - 1)
To find the value of A;
3x + 8 = 0
x = -8/3
To find the value of B;
x - 1 = 0
x = 1
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Describe in words two ratios from the image that are equivalent.
Two ratios from the image that are equivalent to each other are the oranges shapes and the two smaller green shapes.
What are equivalent ratios ?When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1: 3 and 2: 6 are equivalent.
In this case, the two orange shapes are equivalent because they are the same size seeing as they both occupied the same portions of the green and white shapes. The smaller green shapes are also equivalent as they have the same length and width.
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What is the value of x? enter your answer in the box. X = cm a bow tie shape polygon made of two bow ties that share a vertex. The shape is created by two segments intersecting forming two triangles with vertical angles. An alternate interior angle of the triangles are marked congruent to each other. The larger triangle is on the left and the smaller triangle is on the right. In the larger triangle, the left side of the triangle is 32 centimeters. The south side of the triangle is 40 centimeters. On the smaller triangle, the right side of the triangle is 4 centimeters. The north side of the triangle is labeled x.
By proving the two triangles as similar triangles , the value of x in the triangles is x = 5 cm .
By using the proportions, for the two triangles which are similar because they contain three equal angles ;
The One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and
the third angle one has to be same because of the sum of the three internal angles of a triangle must equal 180 degrees.
So , the proportions of the sides are written as :
⇒ 4/32 = x/40 ;
Cross multiplying , and solving for "x" ,
we get ;
⇒ x = (4 × 40)/32 ;
⇒ x = 5 .
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The given question is incomplete , the complete question is
What is the value of x in the polygon given below ?
Mrs. Hamada has 15 paintbrushes and wants to put the same number into each of 5 water cups. Complete the equation below to show how many paintbrushes will be in each cup.
Answer:
3 paintbrushes
Step-by-step explanation:
15 divided by 5 is 3.
So, Mrs. Hamada will put 3 paintbrushes in each cup.
Assuming that b is positive, solve the following equation for b.
b
S
- 1
b≈
(2x-6)dx=13 Round your final answer to 4 decimal places.
(Give the positive answer only.)
The value of b is given as follows:
b = 8.4.
How to obtain the value of b?The value of b is obtained solving the definite integral in this problem.
The integral of the function 2x - 6 is given as follows:
x² - 6x.
At x = b, the numeric value of the integral is given as follows:
b² - 6b.
At x = -1, the numeric value of the integral is given as follows:
(-1)² - 6(-1) = 1 + 6 = 7.
Applying the Fundamental Theorem of Calculus, the equation to obtain the value of b is given as follows:
b² - 6b - 7 = 13.
b² - 6b - 20 = 0.
Which is a quadratic function with the coefficients given as follows:
a = 1, b = -6 and c = -20.
The discriminant is given as follows:
D = b² - 4ac
D = (-6)² - 4(1)(-20)
D = 116.
Hence the positive solution is given as follows:
b = (-b + sqrt(D))/2a
b = (6 + sqrt(116))/2
b = 8.4.
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Based on previous sales, Ron predicted sales of 80 pen sets. He actually sold 100 pen sets. Find the error and absolute error for the pen sets. A 5-column table with 3 rows. Column 1 is labeled Item with entries folders, erasers, pen sets. Column 2 is labeled Approximate Value with entries 25, 220, 80. Column 3 is labeled Exact value with entries 30, 200, 100. Column 4 is labeled Error with entries negative 5, 20, a. Column 5 is labeled Absolute Error with entries 5, 20, b.
The error is 20 and absolute error for the pen sets is also 20. Absolute error is the difference between a quantity's observed or inferred value and its actual value.
What is a absolute error statement?Absolute error is the difference between such a quantity's observed or assumed value and its real value. Because it doesn't indicate the error's magnitude, the absolute inaccuracy is insufficient.
What are absolute and relative error?The difference between a quantity's measured value and its actual value is known as absolute error. The difference between the measurement's absolute error and the quantity's actual value is referred to as relative error.
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Answer:
15%
Step-by-step explanation:
flip edge
100 POINTS BRAINLIEST A business buys equipment with $300 cash and puts $425 on credit. What is the value of this asset?
A. $725
C. $425
B. $300
D. $125
Answer: A) $725
Step-by-step explanation:
The value of the asset that the business bought with $300 cash and $425 on credit is $725. The total amount that the business spent on the equipment is equal to the sum of the cash and the credit, which is $300 + $425 = $725.
HELP ASAP TIMED!! hurry
Answer:
3rd choice (x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - -8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
Please help!! Number 7
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Solving For #7
We will use the Angle Bisector Theorem
The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS
According to the angle bisector theorem:
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]
Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]
If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]
At Hometown Hospital, the cancer registrar recorded the age (at the time of initial diagnosis) of patients diagnosed with lung cancer. A total of 68 cases were recorded. The ages are ranked from oldest to youngest. 91 86 83 82 81 80 80 79 78 77 76 75 75 74 74 73 73 72 72 72 71 71 70 70 70 70 69 69 68 68 67 67 67 66 66 66 66 66 65 65 65 64 64 63 63 62 62 61 61 61 60 60 59 59 59 58 58 57 57 57 56 56 55 54 53 53 52 51 Complete the frequency distribution table with the following data: All score limit ranges Frequency Cumulative frequency Relative frequency [round to two decimal places] Frequency percentage [should be a whole percentage without decimals]
On solving the provided question, we can say that Frequency Percentage is equal to the relative frequency times one hundred.
what is frequency distribution?In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9.
25–29 is listed as the First Class Group.
Class size is 4 (29-25).
Maintain the same class size for reminders from 89 through 93.
Count the values and record the frequency next to the appropriate class.
Midpoint equals (higher class limit plus lower class limit) / 2.
Relative Frequency is equal to Frequency/total Values.
Cumulative Frequency equals the sum of the past and current frequencies.
Frequency Percentage is equal to the relative frequency times one hundred.
Class Recurrence Point Midway Frequency relative Frequency Added Up percentage of frequency 25-29 0 27 0 0 0.00% 1.25% 1 31 0.0125
%ile Rank for 48 = 12.5
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prove that sin51 + sin81 - cos21 = 0
Answer:
Step-by-step explanation:
To prove that sin(51) + sin(81) - cos(21) = 0, we can use the trigonometric identity:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
We can rewrite 51 and 81 as the sum of two angles:
51 = 45 + 6
81 = 90 - 9
Using the above identity, we can write:
sin(51) = sin(45 + 6) = sin(45)cos(6) + cos(45)sin(6) = (2/2)sin(6) + (2/2)cos(6) = sin(6) + cos(6)
and
sin(81) = sin(90 - 9) = sin(90)cos(9) - cos(90)sin(9) = 0 + (-1)sin(9) = -sin(9)
Finally,
sin(51) + sin(81) - cos(21) = sin(6) + cos(6) - sin(9) - cos(21) = (sin(6) + cos(6)) - (sin(9) + cos(21))
We know that sin(90 - x) = cos(x) and cos(90 - x) = sin(x), so we can rewrite the right-hand side as:
(sin(6) + cos(6)) - (cos(90 - 9) + sin(90 - 21)) = (sin(6) + cos(6)) - (cos(9) + sin(69))
We also know that sin(180 - x) = -sin(x) and cos(180 - x) = -cos(x), so we can rewrite the right-hand side as:
(sin(6) + cos(6)) - (cos(9) + -sin(111)) = (sin(6) + cos(6)) - (-sin(111) + cos(9))
Since sin(6) + cos(6) = sin(6 + 90) = sin(96) and -sin(111) + cos(9) = sin(69 - 180) = -sin(111), we can simplify the expression further to:
sin(6) + cos(6) - (-sin(111)) + cos(9) = sin(96) + cos(9)
Since sin(x + y) = sin(x)cos(y) + cos(x)sin(y), we can write:
sin(96) + cos(9) = sin(60)cos(36) + cos(60)sin(36) = (2/2)sin(36) + (√3/2)cos(36) = sin(36) + (√3/2)cos(36)
Finally, since sin(2x) = 2sin(x)cos(x), we can write:
sin(36) + (√3/2)cos(36) = 2sin(18)cos(18) + (√3/2)cos(36) = 2(√2/2)(√2/2) + (√3/2)(√2/2) = (√2 + √6)/2 + (√6/2) = (√2 + √6)
So, sin(51) + sin(81) - cos(21) = (√2 + √6) ≠ 0.
Therefore, we have shown that sin(51) + sin(81) - cos(21) ≠ 0, and the statement "sin(51) + sin(81) - cos(21) = 0" is false.
Hey what is 10(4/24 - 9) - 7.45
Answer
[tex] - 95.783[/tex]
The function, y=-16x^2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground
x=___seconds
Answer: 3
Step-by-step explanation:
Took the test
Amelia and Lucas' son Weights 38.3 pounds. one kilogram is equal to approximately 2.2 pounds Convert their son's weight to kilograms.
Amelia and Lucas' son's weight is 17.41 kilograms.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 km = 1000 m
We have,
Amelia and Lucas' son's Weight = 38.3 pounds.
1 kilogram = 2.2 pounds
Multiply 38.3/2.2 on both sides.
17.41 kilograms = 38.3 pounds
Thus,
Amelia and Lucas' son's weight is 17.41 kilograms.
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The Leswaygo Times is a newspaper in the imaginary country Leswaygo. You read in one of its online articles that the people are unhappy with their new king. He is making changes to make Leswaygo more modern. He believes this will benefit the country, but the people do not agree. They are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to
communism
democracy
autocracy
socialism
Since they are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to: B. democracy.
What is democracy?In Government, democracy can be defined as a type of government that is established by the people and generally for the people. This ultimately implies that, a democracy refers to a type of government that accords all the power to the people.
This simply means that, that the form of power that is exercised through the people is generally referred to as democracy. Additionally, all the people living in a country that practice democracy are expected to elect legislators at large and have a voice in any major decisions through voting.
In this context, we can infer and logically deduce that Leswaygo form of government would be changed to democracy.
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Answer:
I took the quiz it was B democracy
Step-by-step explanation:
It was democracy because that is the strongest form of government
(Q) John has 25 red marbles, 15 blue marbles and 10 yellow marbles. He wants to make similar groups using all the marbles.
(a) Work out the highest number of groups he can make.
(b) Also work out how many, of each color marble, will be in each group.
Answer:
(a) highest number of groups = 5
(b) out how many, of each color marble, will be in each group.
5 red
3 blue
2 yellow
Step-by-step explanation:
The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers
GCF of 25, 15 and 10 can be found as follows by finding factors of each number:
25 = 5 x5
15 = 5 x 3
10 = 5 x 2
Choose the highest number that is common in each group and this is 5
So John can make a maximum number of 5 groups
Divide each number by the GCF to find how may in each group
25/ 5 = 5 red marbles
15/5 = 3 blue marbles
10/5 = 2 yellow marbles
So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles
plsss help i really need it
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
First, we need to know the conversion rate between the two units (pounds lb and kilograms kg)
1 pound = 0.45359237 kilogramsNow, we can convert 90 pounds.
90 × 0.45359237 = 40.8233133 kgSo, 90lb ≈ 41kg
(If you were to round)
Rounded to 3 decimal places, what is the value of r for this data set?
The correlation coefficient r of the data given is 0.938
What is the correlation coefficient?The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables.
Given that a set of data showing the values of variables x and y, we are asked to find the correlation coefficient r of the data given,
We know that,
The correlation coefficient r is a number between and calculated to represent the linear dependence of two variables or sets of data.
Using an Excel tool :- (CORREL function) = CORREL(B3:B10,C3:C10)
We get, r = 0.938
Hence, the correlation coefficient r of the data given is 0.938
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convert the following measurement
The value of expression after change its measurement as;
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
What is Measurement unit?A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The expression is,
⇒ 3.4 × 10⁵ g . cm² / s²
Now, We know that;
⇒ 1 cm = 1/1000 m
⇒ 1 cm = 1/10³ m
⇒ 1 g = 1/1000 kg
⇒ 1 g = 1/10³ kg
Hence, We get;
⇒ 3.4 × 10⁵ g . cm² / s²
⇒ 3.4 × 10⁵ (1/10³) kg . (1/10³)² m²/ s²
⇒ 3.4 × 10⁵ × 10⁻³ × 10⁻⁶ kg . m²/ s²
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
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There are 20 packs of cookies with 10 in each. If these are shared equally among 8 children. How each child get?
Answer: 25 per child
Step-by-step explanation:
20 x 10 = 200
200/8 = 25
20% discount on $365 purchase
Answer:
To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.
Discount = $365 × 0.20 = $73
So, the discount on a $365 purchase is $73.
The price after the discount would be $365 - $73 = $292.
To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:
1. Calculate the discount amount:
Discount = 20% x $365 = $73
2. Subtract the discount from the original price:
Final price = $365 - $73 = $292
Therefore, the final price of the $365 purchase with a 20% discount is $292.
How to I arrive at this number using a common factor?
The common factor is 6[tex]e^{6x}[/tex] (2x - 5)⁸.
What is a common factor?
These are the "common factors" when we determine the factors of two or more numbers and discover some of those factors are the same (or "common").
Given that
d/dx[[tex]e^{6x}[/tex](2x - 5)⁹]
The formula of the product rule is d/dx(uv) = uv' + vu'.
=(2x - 5)⁹d/dx([tex]e^{6x}[/tex]) + [tex]e^{6x}[/tex]d/dx(2x - 5)⁹
Now applying the formula d/dx(x^n) = nx^(n-1), d/dx e^(mx) = m e^(mx)
=(2x - 5)⁹ 6[tex]e^{6x}[/tex] + [tex]e^{6x}[/tex]×2×9 × (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁹ + 18[tex]e^{6x}[/tex](2x - 5)⁸
Now taking common 6[tex]e^{6x}[/tex] (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [(2x - 5) + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [2x - 5 + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸(2x - 2)
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