The solutions of the given functions are:
f(g(x)) = x+10√x+26 and g(f(x)) = √(x²+6)
f(x) = x²+1, g(x) = √x+5 are given.
To find f(g(x)), we need to substitute g(x) into the function f(x):
f(g(x)) = f(√x+5) = (√x+5)²+1 = x+10√x+26
To find g(f(x)), we need to substitute f(x) into the function g(x):
g(f(x)) = g(x²+1) = √(x²+1+5) = √(x²+6)
Therefore, the simplified answers are:
f(g(x)) = x+10√x+26
g(f(x)) = √(x²+6)
Note: It is important to include the parentheses when substituting one function into another to ensure the correct order of operations.
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please help me out with this and i will give u brainy if u give me the right answer
Question 1
What is the mean of the data set?
684, 615, 648, 598, 654, 612, 606, 621, 642, 689
Answer:
Step-by-step explanation:
The mean is 636.9, I got you brotha
Answer:
636.9
Step-by-step explanation:
684+615+648+598+654+612+606+621+642+689
=6369
6369÷10=636.9
I need help solving theses questions
The value of x is 3 and the sides of given rectangle are 3,3,9,9.
What is Area of rectangle ?
area of rectangle can be defined as product of length and breadth.
From the given figure ,
it is given that ,
perimeter of rectangle = 24 cm
and the sides are ,
x,x,x+6,x+6
so we know that perimeter of rectangle = 2 (l+b)
that is,
24 = x+x+x+6+x+6
24 = 4x + 12
4x = 12
x = 3
Therefore, The value of x is 3 and the sides of given rectangle are 3,3,9,9.
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On a winter day adnan look up the current temperature in three nearby cities a adnan chooses two of the temperatures and writes a comparison what are all the possible compare says he can write
There are 9 possible comparisons that Adnan can write using the temperatures of the three nearby cities.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
Let's say that Adnan looks up the current temperature in three nearby cities and writes down their temperatures as T1, T2, and T3.
To compare the temperatures, Adnan can choose any two of the temperatures and write a comparison of them.
Since there are three temperatures, there are a total of three possible pairs of temperatures that Adnan can choose:
1. T1 and T2
2. T1 and T3
3. T2 and T3
For each pair of temperatures, Adnan can write a comparison in one of three ways:
T1 is greater than T2 (T1 > T2)
T1 is less than T2 (T1 < T2)
T1 is equal to T2 (T1 = T2)
So, Adnan can write a total of nine possible comparisons of the temperatures:
T1 > T2,
T1 < T2,
T1 = T2,
T1 > T3,
T1 < T3,
T1 = T3,
T2 > T3,
T2 < T3, and
T2 = T3.
These are all the possible comparisons that Adnan can write using the temperatures of the three nearby cities.
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Find the eigen values and eigen vectors of the matrix A=([2,2,0],[2,1,1],[-7,2,-3]).
The eigen values of the matrix A are 2, -2, and 7, and the corresponding eigen vectors are [1,1,2], [1,-2,0], and [2,1,1].
To find the eigen values and eigen vectors of the matrix A=([2,2,0],[2,1,1],[-7,2,-3]), we first need to find the characteristic equation of the matrix. This is done by finding the determinant of (A-λI), where λ is the eigenvalue and I is the identity matrix.
The characteristic equation is:
|A-λI| = |[2-λ,2,0],[2,1-λ,1],[-7,2,-3-λ]| = 0
Expanding the determinant, we get:
(2-λ)((1-λ)(-3-λ)-2) - 2(2(-3-λ)+7) + 0 = 0
Simplifying the equation, we get:
-λ³ + 6λ² - 5λ - 14 = 0
The eigen values are the roots of this equation. We can use the rational root theorem to find the possible rational roots of the equation, which are ±1, ±2, ±7, and ±14. By testing these values, we find that the eigen values are λ=2, λ=-2, and λ=7.
Now, we can find the eigen vectors by plugging the eigen values back into the equation (A-λI)v=0, where v is the eigen vector.
For λ=2, we get:
([2-2,2,0],[2,1-2,1],[-7,2,-3-2])v = 0
([0,2,0],[2,-1,1],[-7,2,-5])v = 0
The eigen vector for λ=2 is v = [1,1,2].
For λ=-2, we get:
([2+2,2,0],[2,1+2,1],[-7,2,-3+2])v = 0
([4,2,0],[2,3,1],[-7,2,-1])v = 0
The eigen vector for λ=-2 is v = [1,-2,0].
For λ=7, we get:
([2-7,2,0],[2,1-7,1],[-7,2,-3-7])v = 0
([-5,2,0],[2,-6,1],[-7,2,-10])v = 0
The eigen vector for λ=7 is v = [2,1,1].
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Adam has 18 counters he gives 10 counters to lesley what fraction of the 18 counters does lesley give your answer in its simplest form
Lesley has 5/9 of the counters that Adam initially had.
What is the fraction?An element of a number or any number of equal parts is represented by a fraction. There is a fraction with an upper value (numerator) and a lower value (denominator) (lower value).
Ten of the 18 counters that Adam had were given to Lesley. Lesley currently possesses 10 counters.
We must divide Lesley's total number of counters by Adam's starting total number of counters in order to determine the proportion of the 18 counters that Lesley has:
Lesley has 10/18 counters, which is her percentage.
By dividing the numerator and denominator by their 2 greatest common factor, we may simplify this fraction:
Lesley has a fraction of the counters she needs: (10 ÷ 2) / (18 ÷ 2) = 5/9
Lesley now owns 5/9 of the counters that Adam started with.
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Hilda is working with equations of the form x^2 + y^2 + ax = 0
a) What is the equation for these circles in standard form?
b) What is the center point and radius (use fractions if necessary)
c) Consider x2 + y2 + 9x = 0 What is the center point and radius (use fractions if necessary)
(a) The standard form of the equation of the given circle is (x + a/2)² + y² = (a/2)².
(b) The center point and radius of the circle is (-a/2, 0) and a/2, respectively.
(c) The center point and radius of the circle (-9/2, 0) and 9/2, respectively.
a) The equation for these circles in standard form is (x + a/2)² + y² = (a/2)². This is derived from the given equation by completing the square for the x term.
b) The center point of these circles is (-a/2, 0) and the radius is a/2. This can be seen from the standard form of the equation, where the center point is (h, k) and the radius is r in the equation (x - h)² + (y - k)² = r².
c) For the equation x² + y² + 9x = 0, the center point is (-9/2, 0) and the radius is 9/2. This is found by completing the square for the x term and comparing it to the standard form of the equation for a circle.
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How many coefficients are in the
expression
5x - 3y - z + 8?
a.
1
b. 2
C. 3
d. 4
Answer:
c. 3
Step-by-step explanation:
A plus advertising charges a fee of $24 plus $0. 10 per flyefr to print and delever flyers. Print and more charges $0. 25 per flyer. For how many flyers is the cost at a-plus advertising less than the cost of print andff more
The cost of A Plus Advertising will be less than the cost of Print and More if the number of flyers to be printed and delivered is greater than 160.
Let's assume that the number of flyers to be printed and delivered is "x".
The cost of A Plus Advertising can be represented as:
Cost_A = 0.10x + 24
The cost of Print and More can be represented as:
Cost_P = 0.25x
To find out for how many flyers the cost of A Plus Advertising is less than the cost of Print and More, we need to set up an inequality:
Cost_A < Cost_P
0.10x + 24 < 0.25x
Subtracting 0.10x from both sides, we get:
24 < 0.15x
Dividing both sides by 0.15, we get:
160 < x
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2b Every point is in one of the four quadrants. True or False.
2c The abscissa of an ordered pair is always positive. True or false.
Pls help I need this on rsm and get it correct
An abscissa is a line that is drawn perpendicular to the vertical axis, or y-axis, of a graph. It is usually measured in the form of a number, and it is used to determine the position of points, lines, and shapes on a graph. Abscissas are also referred to as the x-coordinates of a graph, and they can be used to plot and analyze data.
What are quadrants?Quadrants are the four sections of a coordinate plane formed by the intersection of the x-axis and the y-axis. Quadrants are labeled I, II, III, and IV, with Quadrant I being the upper right-hand corner, Quadrant II being the upper left-hand corner, Quadrant III being the lower left-hand corner, and Quadrant IV being the lower right-hand corner. Quadrants are commonly used to graph equations and to identify points on a coordinate plane.
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Assume that you are investing $100 for 4 years. Which of the following would get you the most money? Justify your answer.
a. 6.3% interest rate compounded daily b. 6.5% compounded annually
Answer:
The 6.5% compounded annually would get you the most money. This is because, when compounded annually, the interest is calculated on the original sum plus the interest already earned. Over the four year period, this would result in total interest earned being higher than if the interest was compounded daily, as the interest earned each day would be calculated on the original sum only. For example, with a 6.5% compounded annually rate, at the end of the fourth year you would have a total of $127.82, whereas with a 6.3% compounded daily rate, you would have a total of $126.56
Step-by-step explanation:
Anika has great success baking cupcakes and has decided to open a small bakery.Five years ago her grandmother left her R180000 which she invested at 9.5% compound interest per year for 5 years.
she wants to use this money to start her bakery.
Anika has R283362.97 after 5 years of compound interest. She can use this money to start her bakery.
Anika invested, R180000 at 9.5% compound interest for 5 years. To find out how much money she has now, we need to use the formula for compound interest:
A = P(1 + r)^t
Where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. Plugging in the values we have:
A = R180000(1 + 0.095)^5
A = R180000(1.095)^5
A = R180000(1.574)
A = R283362.97
So Anika has R283362.97 after 5 years of compound interest. She can use this money to start her bakery.
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Let the statements p and q be defined as follows:
p = "You mowed the lawn."
q = "You left the room a mess."
Translate the following symbolic statement into words:
Its means that either statement p is false or statement q is true
The symbolic statement that needs to be translated into words is not provided in the question. However, I will provide an example of how to translate a symbolic statement involving the statements p and q into words.
Example: p ∧ q
This symbolic statement can be translated into words as follows: "You mowed the lawn and you left the room a mess." The symbol ∧ represents the logical conjunction "and", which means that both statements p and q are true.
Another example: ¬p ∨ q
This symbolic statement can be translated into words as follows: "You did not mow the lawn or you left the room a mess." The symbol ¬ represents the logical negation "not", and the symbol ∨ represents the logical disjunction "or", which means that either statement p is false or statement q is true.
I hope this helps! If you have a specific symbolic statement that you need help translating, please provide it in the question and I will be happy to help.
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Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining the given points into four equal parts. (a) \( (3,-1),(5,-2) \) \[ \begin{array}{l} (x, y)=( \\ (x, y)
The three points that divide the line segment joining the given points into four equal parts are \((3.5, -1.25)\), \((4, -1.5)\), and \((4.5, -1.75)\)
To find the three points that divide the line segment joining the given points into four equal parts, we can use the Midpoint Formula repeatedly. The Midpoint Formula is given by:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Let's first find the midpoint of the given line segment:
\[ \text{Midpoint} = \left( \frac{3 + 5}{2}, \frac{-1 + (-2)}{2} \right) = \left( 4, -1.5 \right) \]
Now we can use the Midpoint Formula again to find the two other points that divide the line segment into four equal parts. Let's first find the midpoint of the line segment joining the points \((3, -1)\) and \((4, -1.5)\):
\[ \text{Midpoint} = \left( \frac{3 + 4}{2}, \frac{-1 + (-1.5)}{2} \right) = \left( 3.5, -1.25 \right) \]
And then let's find the midpoint of the line segment joining the points \((4, -1.5)\) and \((5, -2)\):
\[ \text{Midpoint} = \left( \frac{4 + 5}{2}, \frac{-1.5 + (-2)}{2} \right) = \left( 4.5, -1.75 \right) \]
So the three points that divide the line segment joining the given points into four equal parts are \((3.5, -1.25)\), \((4, -1.5)\), and \((4.5, -1.75)\).
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The shoe sizes of a group of middle school girls are shown. 5.5 6 7 8.5 6.5 6.5 8 7.5 8 5 If a shoe size of 9 is added to the data, how does the median change? The median stays 6.75. The median increases to 6.75. The median stays 7. The median increases to 7.
Answer:
The median is the middle value when a set of data is arranged in order from smallest to largest.
First, let's arrange the given shoe sizes in order:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5
The median of this data set is 6.5 because it is the middle value.
Now, let's add a shoe size of 9 to the data set:
5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9
The new median of this data set is 7, which is greater than the previous median of 6.5.
Therefore, the answer is: The median increases to 7.
Answer: The median increases to 7.
Step-by-step explanation: I took the test and got a 100%
Please help this is Algebra
According to this data, 36 people selected their favorite colors, fill in the blanks below:
A professor records the following final grades in one course. Construct a frequency table for the grades.
A
A
A
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
D
D
D
D
F
Complete the table.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Grade Frequency Relative Frequency Cumulative Frequency
A. ____ ____% _____
B ____ _____% ______
C ____ _____% ______
D ____ _____% ______
F ____ _____% ______
TOTAL. ____. 1=100%. _______
The frequency table when constructed is
Grade Frequency Relative Frequency Cumulative Frequency
A 3 12.5% 3
B 8 33.3% 11
C 8 33.3% 19
D 4 16.7% 23
F 1 4.2% 24
Total 25 1 or 100%
How to construct the frequency tableThe grades A to F represent the given parameter
From the given grade, we have the following frequencies
A = 3
B = 8
C = 8
D = 4
F = 1
From the above frequency, we have the relative frequency to be
A = 3/24 = 12.5%
B = 8/24 = 33.3%
C = 8/24 = 33.3%
D = 4/24 = 16.7%
F = 1/24 = 4.2%
From the above frequency, we have the cumulative frequency to be
A = 3
B = 11
C = 19
D = 23
F = 24
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HELP ME PLEASE!!!!!!!!!!!!!!!
Answer: 480
Step-by-step explanation: Since this is a triangle, we are using 1/2 * base * height. So since the height is 15, and the base is 64, that would equal 960. Then we are going to divide it by 2, which equals 480.
PLEASE HELP ASAP
Question 2(Multiple Choice Worth 2 points)
(Line of Fit LC)
A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 7 and 3 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 8 and 5 comma 6
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 2 comma 5 and 4 comma 4
scatter plot with points plotted at 1 comma 7, 1 comma 8, 2 comma 5, 3 comma 6, 4 comma 4, 5 comma 5, 5 comma 6, 6 comma 3, 7 comma 5, 8 comma 2, 9 comma 4, and 10 comma 2, with a line drawn through about 1 comma 4.5 and 2 comma 4.5
The scatter plot indicates that the best graph with a line that fits the data is one with a line passing through approximately 2 comma 5 and 4 comma 4.
What is a scatter plot and how is it solved?Data visualisation that demonstrates the link between various variables is known as a scatter plot. Different data points are positioned between an x- and y-axis to display this data. Each of these data points appears to be "scattered" across the graph, which is how this kind of data visualisation gets its name.
This is because the main trend of the data, which seems to slope downwards, is captured by the line that passes through these places. The other lines don't seem to cover as many points or represent the data trend as effectively.
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A parallelogram has a height of 2 units. One side of the parallelogram is AB¯¯¯¯¯. The paralleogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment on the grid represents 1 unit.
Keyboard Instructions
Initial graph state
The horizontal axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
The vertical axis goes from 1.5 to 6.5 with ticks spaced every 1 unit(s).
Point with coordinates (2, 3) labelled: A.
Point with coordinates (5, 3) labelled: B.
It is a unique variety of quadrilateral called a parallelogram that has both pairs of opposite sides parallel and equal.
What is quadrilateral?A polygon with has four sides, four angles, and four vertices is called a quadrilateral. The Latin words 'Quadri', which denotes four, and latus, which means side, were combined to form the English word quadrilateral.
Given, Height of the Parallelogram = 2 units
Each segment on the grid is represented as = 1 unit.
So, One side of the Parallelogram = 3 units
Properties of Parallelogram
a. Opposite sides are equal.
b. Opposite sides are parallel.
c. Diagonals Bisect each other.
Also, Every Rectangle is a Parallelogram.
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The area of a dog kennel is 20 square feet. If the length of the kennel is 4 feet, what is the width of the kennel?
Answer:it would be 25
Step-by-step explanation:
There are 50 millipedes in an area of rainforest. The number of millipedes is expected to increase by 62% every year compared to the year before.
a) how many millipedes are expected to be in the area of rainforest in 5 years time ?
b) how many millipedes are expected to be in the area of rainforest in 20 years time ? Round your answers to the nearest 100.
There are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.
What is percentage growth rate?
The exponential function with a growth factor has a rate greater than 1
We can use the formula for exponential growth to answer this question:
P(t) = P₀(1 + r)ᵗ
where P₀ is the initial population, r is the annual growth rate as a decimal, t is the number of years, and P(t) is the population after t years.
a) For the first part of the question, we can plug in the given values and solve for P(5):
P₀ = 50
r = 0.62
t = 5
P(5) = 50(1 + 0.62)⁵ ≈ 763
Therefore, there are expected to be about 763 millipedes in the area of rainforest in 5 years time.
b) For the second part of the question, we can plug in the given values and solve for P(20):
P₀ = 50
r = 0.62
t = 20
P(20) = 50(1 + 0.62)²⁰ ≈ 225,000
Therefore, there are expected to be about 225,000 millipedes in the area of rainforest in 20 years time. Rounded to the nearest 100, this is 225,100.
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In Exercises 3-6, find the indicated measure. Explain your reasoning. Show your work
The measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
What are similar triangles?Two triangles are similar if the ratio of their corresponding sides is same and their corresponding angles are equal.
Given are the triangles as shown in the image.
{ 1 } -
We can write -
GH/HJ = GK/KJ
GH/4.6 = 3.6/3.6
GH = 4.6
{ 2 } -
QT/TS = QR/RS
4.7/4.7 = QR/1.3
QR = 1.3
{ 3 } -
AD/DC = AB/BC
AD/AD = AB/BC
AB/BC = 1
5x/4x + 3 = 1
5x = 4x + 3
x = 3
AB = 15
{ 4 } -
UW/UV = DW/DV
7x + 13 = 9x + 1
3x = 12
x = 4
UW = 41
Therefore, the measured unknown sides are -
GH = 4.6
QR = 1.3
AB = 15
UW = 41
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The heights of 14 plants, in inches, are listed. 12,14, 15, 15, 16, 16, 16, 17, 18, 19, 20,22,25 If another plant with a height of 174inches is added to the data, how would the mean be impacted? The mean would stay the same value of 17.1 inches. The meam would stay the same value of 17.4 inches. The range would increase to 17.4 inches. The range would decrease to 17.4 inches
Answer:30.69230769 in decimal form
399/13 in percent form
30 9/13 in fraction form
These are all the means in different forms.
Step-by-step explanation:
The Amador family pays $7.50 per thousand cubic feet of natural gas. The total cost, t, varies directly as the number of thousand cubic feet of natural gas, g, used.
The constant of proportionality for the Amador family is obtained as k = 7.50.
What is a COP?The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If the cost t varies directly with the number of thousand cubic feet of natural gas g used, we can write -
t = kg
where k is the constant of proportionality, which represents the cost per thousand cubic feet of natural gas.
Since the Amador family pays $7.50 per thousand cubic feet of natural gas, we have -
k = 7.50
Therefore, the equation relating the total cost t to the number of thousand cubic feet of natural gas g used is -
t = 7.50g
This means that for every thousand cubic feet of natural gas used, the cost is $7.50.
If the Amador family uses 10,000 cubic feet of natural gas, the total cost would be -
t = 7.50(10) = $75
If they use 20,000 cubic feet of natural gas, the total cost would be -
t = 7.50(20) = $150
Therefore, the COP value is k = 7.50.
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Twenty people are put into an insurance pool. Of these twenty people, • 12 people each have expected payouts of $4,500 per year. 5 people each have expected payout of $12,300 per year. • 2 people each have expected payouts of $20,800 per year. • 1 person has an expected payout of $30,900 per year. How much is the average expected payout for each member of the group of twenty? Average Expected Payout is $
Answer:
the average payout should be $157,100
hope this helps <3
During a recent telethon, people pledged $25 or $50. Twice as many people pledged $25 as $50. Altogether, $18,000 was pledged. How many people pledged $25?
Answer:
360 people pledged $25.
Step-by-step explanation:
You'll need to set up only one equation to solve this.
Let's use x for the number of people who pledged $50. Since twice as many people pledged $25, it would be 2x. Keep this in mind for later.
Multiply 2x by 25, and you should get 50x. Now, your equation is 50x + 50x = 18,000. Simplify this to 100x = 18,000.
Now, divide both sides by 100. After doing so, you should have x = 180. This is how many people pledged $50. To find how many pledged $25, plug the value of x into 2x. (In other words, multiply 180 by 2.) After doing so, you should get 360. This is how many people pledged $25.
Hope this helps!
16X12=102
According to the food label on a box cookies, each box has 16
servings and each serving contains 4 cookies. The weight of the
box of cookies is kilograms. What is the weight of each
cookie?
Answer: We cannot solve this problem as there is a mistake in the equation you provided.
16 x 12 is not equal to 102. The correct answer is 192.
To find the weight of each cookie, we need to know the total weight of the box of cookies. Let's call the weight of the box "W".
Since there are 16 servings in the box and each serving contains 4 cookies, there are a total of 16 x 4 = 64 cookies in the box.
To find the weight of each cookie, we can divide the total weight of the box by the number of cookies:
Weight of each cookie = W / 64
Without knowing the weight of the box, we cannot determine the weight of each cookie.
Step-by-step explanation:
calculate the surface area of the triangular prism below. Give your answer in mm.
Surface area of the triangular prism which is a compound shape has an area of: 878mm².
What are compound shapes?The combined area of one or more circles and simple polygons is known as the area of the composite forms. The areas of every basic shape can be added together to determine the area of the composite shapes. Simply calculate each shape's area separately, then put them together to get the area of composite shapes.
Now in the question, we have 2 triangles with base, b =31mm and height, h = 14mm
Now area of both the triangles = 2 × 1/2 × b × h
= 2×1/2×14×31
=434mm²
Now we have three different rectangles.
In the first rectangle, length, l = 27mm and breadth, b = 6mm
Area of the rectangle as we know = l × b
= 27 × 6
= 162mm²
In the second rectangle, l = 16mm and b = 6mm
Area = 16 × 6
= 96mm²
In the final rectangle, l = 31mm and b = 6mm
Area = 31 × 6
= 186mm²
Therefore, the total surface area = 162 + 434 + 96 + 186 = 878mm².
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simply:cos195°.cos285°
cos{60°−x}cosx – sin(60°−x)sinx
Answer:
x=0
Step by step explanation:
cos (a+b) = cos(a) cos(b) -sin (a) sin (b)
Same identity forms in question.
L.H.S -cos (x+60)
Now write it in the form of sin .
sin [90-(60+x)]
Equal to RHS
R.H.S - 30
90-(60+x)=30
30-x=30
x=0
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The answer to the equation cos195°cos285° is -1/4.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between different quantities and can be used to solve for unknown values. Equations are typically written as symbols, but can also be written in words. Simple equations might involve addition, subtraction, multiplication, and division, while more complex equations may involve exponents, logarithms, and trigonometric functions. Equations can be used to model and understand real-world phenomena, such as calculating projectile motion, or predicting the behavior of a chemical reaction.
This is derived from the trigonometric identity cos{60°−x}cosx – sin(60°−x)sinx. This identity states that the cosine of the sum of two angles is equal to the product of the cosines of each angle minus the product of the sines of each angle.
By substituting the angles 195° and 285° into the identity, we get cos{60°−195°}cos195° – sin(60°−195°)sinx. When we use the values of the angles, we get cos{-135°}cos195° – sin(135°)sinx. We can then simplify this to -1/4cos195° – 0sinx. As the sine of the angle is 0, this simplifies to –1/4cos195°. As the cosine of 195° is -1/4, the answer to the equation cos195°cos285° is -1/4.
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Cos(x)^2 in terms of sin(x)
Hope this helps! the screenshot is inserted and the explanation and answer are there