To fill the blank of the given table above is represented below as follows:
1= 11.4 grams
2= 22.8 grams
6= 68.4 grams
10 = 114 grams
How to calculate the grams per package?If 2 packages = 22.8 g
1 package = X grams
Make X the subject of formula;
x grams = 22.8/2 = 11.4grams
If 1 package = 11.4 grams
6 packages = y grams
Make y the subject of formula;
y = 6×11.4
y = 68.4 grams
If 1 package = 11.4 grams
z packages = 114 grams
make z the subject of formula;
z = 114/11.4
z = 10 packages.
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find 10% of 140
pls give simple owrking out
Answer:
14.
Step-by-step explanation:
0.10*140 = 14
Cool.
Answer:
14
Step-by-step explanation:
To find a certain percent of a number, you first convert that percent to a decimal, by dividing by 100:
10/100 = 0.1
Then, you take this decimal and multiply it by the number:
0.1*140 = 14
Hope this helped!
Aviv and Marco were trying to describe parts of the expression \dfrac{5a}{2a+3}
2a+3
5a
start fraction, 5, a, divided by, 2, a, plus, 3, end fraction.
Aviv said, "The entire expression is the quotient of 5a5a5, a and 2a+32a+32, a, plus, 3."
Marco said, "On its
own, 2a+32a+32, a, plus, 3 is a sum with 222 terms."
Who is correct?
Choose 1 answer:
The correct option is D. Both students are correct.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is 5a / 2a+3.
When we divide a number with p with another number q, then the resulting value is the quotient of the division of the two numbers.
Here the two expressions are 5a and 2a + 3.
5a / 2a+3 is actually (5a) ÷ (2a+3).
The value of the entire expression is the quotient. So Aviv is correct.
The expression 2a + 3 has two terms, 2a and 3. So Marco is also correct.
Hence the description of both Aviv and Marco are correct.
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The complete question is as follows :
Aviv and Marco were trying to describe the parts of the expression 5a/2a+3.
- Aviv said, "The entire expression is the quotient of 5a and 2a+3"
- Marco said, "On it's own, 2a+3 is a sum with 2 terms."
Who is correct?
Choose one answer:
A: Only Aviv
B: Only Marco
C: Neither student is correct
D: Both students are correct
Fawn, Joey, and Caleb play a board game. Fawn’s score is -28 points. Joey score is 4/7 of Fawns’s score. Caleb scores 3/4 as many points as Joey how many points do they score and all?
Answer:
Fawn's score: -28 points, Joey's score: -16 points, Caleb's score: -12 points. Total score: -56 points.
Step-by-step explanation:
Joey's score:
[tex]\frac{4}{7}*-28=-16[/tex]
Caleb's score:
[tex]\frac{3}{4}*-16=-12[/tex]
Total score:
[tex]-28 + -16+ -12 = -56[/tex]
how many pieces of wood can be cut from a board that is 107/8 feet long is each piece is 227/140 feet long?
The number of pieces of wood that can be cut from the board is 8.
A fraction is a mathematical expression that represents a part of a whole. It is written as two numbers separated by a slash ( / ). The top number, called the numerator, represents the number of parts being considered, and the bottom number, called the denominator, represents the total number of parts in the whole. For example, 1/2 is a fraction that represents one part of a whole that has been divided into two equal parts.
To determine the number of pieces of wood that can be cut from a board that is 107/8 feet long, if each piece is 227/140 feet long, you need to divide the length of the board by the length of each piece.
You can calculate the number of pieces by dividing the length of the board which is 107/ 8 feet by the length of each piece which is 227/ 140 feet:
= 107/ ( 8 * 227/ 140)
= (107/8) * (140/ 227)
= 8.25
= 8
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a deck of cards contains 52 different cards. for each of the following situations, give the number of equally likely outcomes (note: not probabilities.)
A deck of cards contains 52 different cards is 52 = 52 P1
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
a) as there are 52 cards ; and selecting one card from 52 = 52P1 equally likely outcome
b)for order matters ; number of ways =52 P2
=52*51
=2652
c) for order not matter ; number of ways =52 C3
=22100
d) this is similar to problem 2 of having 2 cards from deck ; number of ways =52 P2
=52*51
=2652
e) if order matters ;number of ways =52*52
=2704
52 distinct cards make to a deck of cards, hence 52 = 52 P1
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Michelle made an apple pie. She used 1/6 of a tablespoon of cinnamon and 1/12 of a tablespoon of nutmeg. How much more cinnamon than nutmeg did Michelle use?
Answer:
2 times more
Step-by-step explanation:
1/6= 2/12, 1/12*2 = 2/12=1/6 so Michelle used 2 times more cinnamon than nutmeg
Use the figure. 8 ft Find the area. Use Enter the correct answer in the boxes.for T. ft 2
The area of the circle is 201 1 / 7 ft square.
How to find the area of a circle?The figure above is a circle. The radius of the circle is 8 feet. The area of the circle can be found as follows:
area of the circle = πr²
where
r = radius of the circleπ = 22 / 7Therefore, let's find the area of the circle as follows:
area of the circle = πr²
π = 22 / 7
r = 8 ft
Hence,
area of the circle = 22 / 7 × 8²
area of the circle = 22 / 7 × 64
area of the circle = 1408 / 7
Therefore,
area of the circle = 201 1 / 7 ft²
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The perimeter of a rectangular lawn i 50 meter. It' 16 meter long how wide i it?
The width of the rectangle is 9 meter.
Now, According to the question:
The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.
Now, Solving the problem:
Perimeter of rectangle is 50 meter sq.
Length of the rectangle(L) is 16 meter.
We have to find the width (W) of the rectangle.
We know that,
Perimeter of rectangle is = 2 (L + W)
50 = 2(16 + W)
50 = 32 + 2W
2W = 50 - 32
2W = 18
W = 18/2
W = 9
Hence, The width of the rectangle is 9 meter.
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Part A Find the value of a in the parallelogram.
a=4
a = 17
a=7/3
a=9
Part B What is m Z
48°
64°
116°
132°
Answer:
a = 17∠Z = 116°Step-by-step explanation:
You want the value of 'a' in a parallelogram with opposite sides marked (a+3) and (2-14). And you want the value of an unmarked angle in the same parallelogram with opposite angles marked (4b-56)° and (2b+4)°.
A. SidesOpposite sides of a parallelogram are congruent, so we have ...
XY = WZ
(a +3) = (2a -14)
17 = a . . . . . . . . . . add 14-a
B. AnglesOpposite angles of a parallelogram are congruent, so we have ...
∠Y = ∠W
(4b -56)° = (2b +4)°
2b = 60 . . . . . . . . . . . . add 56-2b
Then angle W is ...
∠W = (2b +4)° = (60 +4)° = 64°
Angle Z is the supplement of angle W, so its measure is ...
∠Z = 180° -64°
∠Z = 116°
__
Additional comment
Adjacent angles in a parallelogram are supplementary.
The population of a city decreae by 3. 4% per year. What hould we multiply the current population by to find next year' population in one tep?
We should multiply the current population by 0.966.
Now, According to the question:
What is the percentage?
The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
"Information available from the question"
The population of a city decrease by 3. 4% per year.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Then the population after one year is given as
P = (100% - 3.4%) of P₀
P = 99.4% of P₀
P = 0.966P₀
Hence, We should multiply the current population by 0.966.
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Solving the following Logarithmic Equation:-
[tex]\mathrm{log_2(x+5)=log_2(1-5x)}[/tex]
The solution to the logarithmic equation log₂( x + 5 ) = log₂( 1 - 5x ) is x = -2/3.
What is the solution to the given Logarithmic Equation?Given the equation in the question;
log₂( x + 5 ) = log₂( 1 - 5x )
Note that, for the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Hence,
x + 5 = 1 - 5x
Solve for x
Move all terms containing x to the left side of the equation.
x + 5 + 5x = 1 - 5x + 5x
x + 5 + 5x = 1
Subtract 5 from both sides
x + 5 - 5 + 5x = 1 - 5
x + 5x = 1 - 5
6x = -4
x = -4/6
x = -2/3
Therefore, the value of x is -2/3.
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Point � E is located at ( − 5 , 1 ) (−5,1) on the coordinate plane. Point � E is reflected over the � x-axis to create point � ′ E ′ . What ordered pair describes the location of � ′ ? E ′ ?
The coordinates of E' is (-5, -1)
What is reflection?A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Given that, a point E (-5, 1) on the coordinate plane, is being reflected over the x-axis to create point E', we need to find the coordinates of E',
The rule of reflection over the x-axis is:
(x, y) → (x, -y)
That mean,
The x coordinates remains same and the sign of y coordinates gets changed,
Therefore,
(-5, 1) → (-5, -1)
Hence, the coordinates of E' is (-5, -1)
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twenty-five soldiers standing side-by-side form a row 22.5 m wide. how many soldiers are marching in a parade when there are 40 rows each 8.1 m wide?
The number of soldiers in the parade is given by the equation A = 360 soldiers
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the number of soldiers in the parade be represented as A
Now , the proportion will be
The number of soldiers in 22.5 m wide row = 25 soldiers
Now , the length of 1 row = 8.1 m
The length of 40 rows = 40 x 8.1 = 324 m
So , 25 / 22.5 = A / 324 be equation (1)
On simplifying the equation , we get
Multiply by 324 on both sides of the equation , we get
A = ( 25 x 324 ) / 22.5
A = 8100 / 22.5
A = 360 soldiers
Therefore , the value of A is 360 soldiers
Hence , the equation is A = 360 soldiers
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Need help with my math homework
Answer:
In the assignment, it says to "Look at the Neverbend Residence Floor Plan on page 8", but you didn't attach an image of the floor plan, so none of the questions can be answered. Please create another question, this time attaching the floor plan.
the maximum number of comparisons that a binary search function will make when searching for a value in a 2,000-element array is: (enter a numeral)
The maximum number of comparisons that a binary search function will make when searching for a value in a 2,000-element array is log₂(2000), which is approximately equal to 11.
The maximum number of comparisons that a binary search function will make when searching for a value in a 2,000-element array can be calculated using the logarithmic time complexity of the binary search.
In a binary search, the array is divided into two halves at each comparison, and the half that contains the target element is selected for the next comparison. This continues until the target element is found or it is determined that the element does not exist in the array.
The maximum number of comparisons can be calculated as the base-2 logarithm of the size of the array, rounded up to the nearest integer. In this case, the size of the array is 2,000 elements, so the maximum number of comparisons is:
log₂(2000) = 10.96...
= 11 comparisons
Therefore, the maximum number of comparisons that a binary search function will make when searching for a value in a 2,000-element array is 11.
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1 Find the derivatives of the exponential functions with respect to x: e 4x e^-2θ
Answer:
Step-by-step explanation:
There are 45 animals in a zoo. 40 of them are tigers.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate.
If x and y are in direct proportion and y is 15 when x is 5, find y when x is 4.
Answer: 25
Step-by-step explanation:
y:x = 15:3 = 5:1
If x is 5, then y = 25
the last term of an arithmetic progression consisting of 12 term is 37 .if the sum of the two middle terms of he progression is 41 then find the arithmetic progression and also the sum of the terms of the arithmetic progression.
Answer: -29, -23, -17, -11, -5, 1, 7, 13, 19, 25, 31, 37
The sum of the terms of the arithmetic progression is 48
Step-by-step explanation:
An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is a constant. The common difference is denoted by d.
Given that the last term of the AP is 37 and there are 12 terms in total, we can use the formula for the nth term of an AP:
an = a1 + (n-1)d
Where a1 is the first term and n is the number of terms.
We know that the last term is 37, so we can substitute in the formula:
37 = a1 + (12-1)d
37 = a1 + 11d
To find the first term, we can subtract 11d from both sides:
a1 = 37 - 11d
The sum of an arithmetic progression is given by the formula:
Sn = n/2(2a1 + (n-1)d)
We know that the sum of the two middle terms is 41, and we can use this information to find the sum of the entire AP:
41 = (12/2)(2a1 + (12-1)d)
41 = 6(2a1 + 11d)
41 = 12a1 + 66d
Now we have two equations with two variables, we can use these equations to solve for the common difference d.
37 = a1 + 11d
41 = 12a1 + 66d
Substitute the first equation into the second equation:
41 = 12(37 - 11d) + 66d
41 = 444 - 132d + 66d
41 = 444 - 66d
Now we can solve for the common difference d:
-66d = -403
d = 6
Now that we know the common difference, we can use it to find the first term:
a1 = 37 - 11d
a1 = 37 - 11(6)
a1 = 37 - 66
a1 = -29
So the arithmetic progression is:
-29, -23, -17, -11, -5, 1, 7, 13, 19, 25, 31, 37
and the sum of the terms of the arithmetic progression is
Sn = 12/2(-29 + 37) = 12/2(8) = 48
The Arithmetic progression is -5, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37 and the sum of the terms of the arithmetic progression is 456.
Let the common difference of the arithmetic progression be d and the first term be a. Then, the 12th term is a + 11d = 37.
The two middle terms of an arithmetic progression with an odd number of terms are the 6th and 7th terms. Thus, the sum of the two middle terms is (a + 5d) + (a + 6d) = 41.
Solving the system of equations:
a + 11d = 37
a + 5d + a + 6d = 41
a = -5, d = 4
So, the arithmetic progression is -5, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37.
To find the sum of the terms, we can use the formula for the sum of an arithmetic series, which is: (n/2)(2a + (n-1)d)
(where n is the number of terms, a is the first term, and d is the common difference.)
So, the sum of the terms is (12/2)(2*-5 + (12-1)4) = 12(-5 + 43) = 12*38 = 456
Therefore, The arithmetic progression is -5, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37 and the sum of the terms of the arithmetic progression is 456.
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somebody help me graph y=(x-2)^3
The graph of the function is added as an attachment
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
y=(x-2)^3
The above expression is a cube function that has been transformed/translated from its parent function to the right by 2 units
Next, we plot the graph
See attachment for the graph of the inequality
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Assuming LIFO, what is the cost of goods sold for the July 7 sale? (Round your final answer to the nearest dollar)
A. $672
B. $670
C. $668
D. $667
The total cost of goods sold for the July 7 sale is $670, calculated using the Last In First Out (LIFO) method.
July 7th sale:
Beginning inventory: $2,000
Purchases:
June 30th: $1,000
July 5th: $600
Cost of goods sold:
June 30th: $1,000
July 5th: $400
July 7th: $270
Total cost of goods sold: $1,670
Ending inventory: $2,000 - $1,670 = $330
Cost of goods sold for July 7th sale: $1,670 - $330 = $1,340
he Last In First Out (LIFO) method is used to calculate the cost of goods sold for a business. This method assumes that the most recently purchased or produced goods are the first to be sold, used, or disposed of. To calculate the cost of goods sold with the LIFO method, the cost of the most recently purchased or produced goods is subtracted from the cost of the goods in inventory.
For the July 7 sale, the cost of goods sold can be calculated by subtracting the cost of goods in inventory ($742) from the cost of the goods purchased on July 7 ($812). This gives us a cost of goods sold of $670. This answer should be rounded to the nearest dollar, so the final answer is $670.
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The complete question is
Assuming LIFO, what is the cost of goods sold for the July 7 sale? (Round your final answer to the nearest dollar) what is the cost of goods sold for the July 7 sale?
A. $672
B. $670
C. $668
D. $667
the 52 cards in a deck are numbered 1, 2, $\dots$, 52. alex, blair, corey, and dylan each picks a card from the deck without replacement and with each card being equally likely to be picked. the two persons with lower numbered cards form a team, and the two persons with higher numbered cards form another team. let $p(a)$ be the probability that alex and dylan are on the same team, given that alex picks one of the cards $a$ and $a 9$, and dylan picks the other of these two cards. the minimum value of $p(a)$ for which $p(a) \ge \frac{1}{2}$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
The value of m = 1 and n = 50, and the answer is (m.n) = 50
Let's call the cards picked by Alex and Dylan "pair 1".
Since Blair and Corey have to pick cards from the remaining 50, there are 50 * 49 = 2400 ways in which Blair and Corey can pick their cards.
Of these, 48 are such that Blair and Corey have the lower numbered cards and form the first team,
And 48 are such that Blair and Corey have the higher numbered cards and form the second team.
Thus, the probability that Alex and Dylan are on the same team is
p(a) = 48/2400 = 1/50
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
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Mr and mr garcia are planning to put new crown molding up around the ceiling in their 8ft x 10ft rectangular bedroom. How much molding will they need?
The length of the molding that Mr. and Mrs. Garcia are to place is:
P = 38ft
What is the perimeter?The perimeter is the sum of the sides of a plane figure, when they are straight, and when they are curved it is the sum of the path of those curves.
If we know that the Garcia family's roof is of the following dimensions:
8ft x 10ft, then evidently it is a rectangular ceiling, and the molding they will place will be around it so its length we determine as the perimeter of a rectangle:
Equation:
P = 2x + 2y
x = 8ft
y = 10ft
P = 2(8ft) + 2(10ft)
P = 38ft
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assuming you have the following data values (6, 1, 3, 7, 2), what is the min-max normalized value for 4.
The min-max normalization formula, the normalized value for 4 is (4-1)/(7-1) = 0.5.
The min-max normalization formula is (x-min)/(max-min). To calculate the min-max normalized value for 4 we need to first calculate the min and max of the given datavalues. The min is 1 and the max is 7. Therefore, using the min-max normalization formula, the normalized value for 4 is (4-1)/(7-1) = 0.5. Min-max normalization is used to scale values in a dataset to a range between 0 and 1. Min-max normalization is a technique used to scale numeric values between 0 and 1. It is useful for data normalization, which helps to bring all the values within a given range. For example, if the data set contains values ranging from 0 to 10, min-max normalization can be used to scale the values between 0 and 1. The formula for min-max normalization is (x - min) / (max - min), where x is the value to be normalized, min is the minimum value in the data set, and max is the maximum value in the data set.This technique ensures that all values in a dataset are scaled to the same range. It is useful when comparing values from different datasets that have different scales.
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i have multiple questions; 1)how are colliding plates connected to earth activity? 2)what does stress on a rock look like? 3)how would you demonstrate shearing? (i couldn't find science in the subjects so i put it under mathematics)
Colliding plates are connected to the earth activities through the lithosphere as it is broken up into plates.
Stress on a rock causes the rock to have a different form.
To demonstrate shearing, you have to carry out the experiments that have been explained.
How are colliding plates connected to earth activity?Colliding plates are connected to Earth activity because they are a major part of plate tectonics, which is the study of how the Earth's lithosphere (crust and upper mantle) moves and deforms. The lithosphere is broken up into several large and small plates that are in constant motion, colliding, sliding past, or moving away from one another. These plate movements can cause earthquakes, volcanic eruptions, and the formation of mountain ranges.
Stress on a rock can manifest in several ways, such as deformation, cracking, or breaking. When a rock is subjected to stress, the rock will change shape or size, creating a state of strain. The rock will also develop fractures or cracks, which are called joints. Stress can also cause a rock to break or shatter, which is called a fault or shear.
To demonstrate shearing, one could take a block of clay or putty and apply a force to one side of the block, pushing it in one direction, while holding the opposite side steady. As the clay or putty is pushed, it will begin to deform, the one side will move in relation to the other side and this movement of one side in relation to the other is called shearing. Another way to demonstrate shearing is to take a rectangular piece of paper and apply force on two opposite corners in opposite direction, this will cause the paper to bend and shear.
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In 1980, the population of Kentucky wa 3. 7 million. If the population grow 23% every decade, what i the population in 2010?
The population of Kentucky in 2010 is 6.3 millions
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
1st data = 19802nd data = 20101st data population = 3.7 million% growth = 23%2nd data population = ?Calculating how many decades have been passed from 1980 to 2010:
1 decade is equal to 10 year
Decades = (2010 - 1980)years * 1 decade / 10 years
Decades = 30/10
Decades = 3 decades
Calculating how much the population have grown:
Growth = 3.7 million * 23/100 * 3 decades
Growth = 2.6 million
Calculating the population in 2010:
2010 population = 3.7 + 2.6
2010 population = 6.3 millions
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ulia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M. Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees. Which best describes the accuracy of Julia’s solution? Accurate. The triangles are similar and the congruent angles are listed in corresponding order. Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º. Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order. Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G. Mark this and return
The solution is Option D.
The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔFGH
Now , the measure of ∠F = 98.6
The measure of ∠G = 61.1
So , the measure of ∠H = 180° - ( ∠F + ∠G ) ( sum of internal angles = 180° )
On simplifying the equation , we get
The measure of ∠H = 20.3
And ,
Let the second triangle be represented as ΔLMN
Now , the measure of ∠L = 98.6
The measure of ∠M = 18.3
So , the measure of ∠N = 180° - ( ∠L + ∠M ) ( sum of internal angles = 180° )
On simplifying the equation , we get
The measure of ∠N = 63.1
So , from the similar triangle theorem ,
The angle M is not congruent to angle H, and angle N is not congruent to angle G
Hence , the triangles are not similar
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katherine spent of her hike going uphill. if she spent hour and minutes hiking uphill, how many hours long was her hike?
Katherine spent 1 hour and 42 minutes hiking uphill, so her hike would be approximately 2.3 hours long.
To calculate how many hours Katherine spent on her hike going uphill, we can use the following steps:
Calculate the total number of minutes Katherine spent hiking uphill by multiplying the number of hours (1) by the number of minutes in an hour (60): 1 * 60 = 60 minutes.Divide the total number of minutes (60) by the number of minutes in an hour (60) to calculate the total number of hours: 60 / 60 = 1 hour.Add the number of hours spent hiking uphill (1) to the total number of hours Katherine spent on her hike (1) to get the total number of hours her hike was: 1 + 1 = 2 hours.Learn more about mathematics:
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a 2016 national public radio report described a study comparing patients who had their first ever traumatic brain injury 18 months earlier with similar healthy individuals with no prior brain trauma. The news report states that, 18 months after their traumatic brain injury, the patients "were still getting, on average, an hour more sleep each night than similar healthy people were getting. And despite the extra sleep, 67 percent showed signs of excessive daytime sleepiness. Only 19% of healthy people had that problem.
a) Identify the individuals in the study.
b) identify the variables recorded and whether they are categorical or quantitative.
The individuals in the study are those who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma. The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical).
a) The individuals in the study are patients who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma.
b) The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical).
a) The individuals in the study are those who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma.
b) The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical). Quantitative variables are those that measure a numerical value, such as sleep duration, while categorical variables are those that measure a characteristic or attribute, such as signs of excessive daytime sleepiness.
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The base of a triangle is eight more than twice its height. If the area of the triangle is 55 square centimeters, find its base and height.
Type an exact number, using radicals as needed.
Answer should be simplified
Please help!
The required base and height are 19.68 centimeter, 5.68 centimeter.
What is area of triangle?Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base. After that, enter the height and base measurements you have into the formula.
According to question:Let the height of the triangle is h
Then base can be written as 2h + 8
Area = 55 square centimeters
Now,
Area = bh/2
55 = h(2h + 8)/2
2h² + 8h = 110
2h² + 8h - 110 = 0
On solving it
h = -2 ± 7.68
h = 5.68 centimeter.
Then base of triangle = 2(5.68) + 8
= 11.36 + 8
= 19.68 centimeter.
Thus, required base and height are 19.68 centimeter, 5.68 centimeter.
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GEOMETRY!!!!!!
Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of Angle ABD.
What is the measure of angle ABD?
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