The length of the hypotenuse of the triangle is 4.1.
Here we have to find the length of the hypotenuse of the triangle.
Data given:
A right triangle has one side that measures 4 in and the angle opposite that side measures 80°
To determine the length of the hypotenuse of the triangle, the trigonometry function can be used.
sinФ = perpendicular/ hypotenuse
sin80° = 4/ hypotenuse
0.98 = 4/ hypotenuse
hypotenuse = 4/ 0.98
Hypotenuse = 4.0617 inch.
Therefore the length of the hypotenuse of the triangle to the nearest tenth is 4.1
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What are 3 rules that prove two triangles are similar?
Three rules that prove two triangles are similar AA, SAS, SSS.
When two shapes in geometry have the same shape but different sizes, they are said to be comparable. A square with sides of 21 cm and one with sides of 14 cm would be comparable. A square with sides of 14 cm and an equilateral triangle with sides of 21 cm are not comparable because they are different shapes.
Applying three triangle-specific theorems makes it simple to distinguish between similar triangles.
In geometry, correspondence refers to the exact relationship between a specific part on one polygon and a part that is similarly positioned on another polygon.
These theorems knows as
Angle-Angle (AA) = Two pairs of corresponding angles are equal.
Side-Angle-Side(SAS) = Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Side-Side-Side(SSS) = Three pairs of corresponding sides are proportional.
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Rotate these ordered pairs around the origin
90° Counter clockwise.
(2,3)
(-4,7)
(5,-4)
(-8,-6)
Answer:
After rotating the ordered pairs 90° counterclockwise around the origin, they will become:
(3, -2)
(-7, -4)
(-4, 5)
(-6, 8)
To rotate a point 90° counterclockwise around the origin, you can use the following transformation matrix:
[[0, -1],
[1, 0]]
To rotate a point (x, y) by 90° counterclockwise, you can multiply the transformation matrix by the point, which will give you the new coordinates of the point after the rotation. For example, to rotate the point (2, 3) 90° counterclockwise, you can multiply the transformation matrix by the point:
[[0, -1],
[1, 0]] * [2, 3] = [3, -2]
Similarly, you can rotate the other points 90° counterclockwise using the same transformation matrix.
~Describe the transformation(s) shown:
A snack food company advertises that they have increased the size of their standard tortilla chips bag to 16.8 ounces, which is 20% more than the original size.
What is the original size of the bag?
A tortilla chip bag labeled x ounces. A tortilla chip bag that has 20 percent more is labeled 16.8 ounces.
The original size of the bag is given by the equation A = 14 ounces
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the original size of the bag be = A
Now , the equation will be
The increased size of the bag = 16.8 ounces
The percentage increase in the size of the bag = 20 %
So , the equation for the percentage increase in the size of the bag is
Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag
Substituting the values in the equation , we get
A + ( 20/100 ) x A = 16.8
( 120 / 100 ) A = 16.8
On simplifying the equation , we get
Multiply by 100 on both sides of the equation , we get
120A = 1680
Divide by 120 on both sides of the equation , we get
A = 14 ounces
Therefore , the value of A is 14 ounces
Hence , The original size of the bag is 14 ounces
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a box with a square base and open top must have a volume of 4,000 cm3. find the dimensions of the box (in cm) that minimize the amount of material used. sides of base cm height
Therefore width = 10cm
height = 20cm
length = 20cm
given that
volume = 4,000[tex]cm^{3}[/tex]
let height = h
width = w
length = l
width and length are equal
height = length = h
volume of box = height × width × height
4000 = h × w × h
4000 = [tex]h^{2}[/tex]w
w = 4000/[tex]h^{2}[/tex]
surface area(SA) = area of base + sum of area of each side
= [tex]h^{2}[/tex] + hw + hw + hw + hw
= [tex]h^{2}[/tex] + 4hw
substitute y = 4000/[tex]h^{2}[/tex]
SA = [tex]h^{2}[/tex] + 4x(4000/ [tex]h^{2}[/tex] )
SA = [tex]h^{2}[/tex] + 16000/h
Taking the derivative:
SA' = 2h - 16000/ [tex]h^{2}[/tex]
making SA' = 0:
0 = 2h - 16000/ [tex]h^{2}[/tex]
2h = 16000/ [tex]h^{2}[/tex]
2[tex]h^{3}[/tex] = 16000
[tex]h^{3}[/tex] = 8000
h = 20 cm
w = 4000 / [tex]h^{2}[/tex] = 4000 / 20² = 10 cm
Therefore width = 10cm
height = 20cm
length = 20cm
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Question 2 (1 point)
(01.01 LC)
Which rational number equals 0.2?
1/10
1/9
2/10
2/9
Answer:
2/10
Step-by-step explanation:
0.2 is 2 tenths. and 2/10 is also two out of ten. two out of ten is two tenths. therefor it is 2/10
Write 45% as a fraction or mixed number in simplest form.
The simplest form is ?
Answer:
9/20
Step-by-step explanation:
hope it helps!
Could you please give me brainliest for this? Thank you!
How do you solve a 2x2 linear system?
The 2x2 linear system can be solved by the method of substitution .
In the question ,
it is given that ,
a 2x2 linear system is the system in which there are 2 equations with two unknown ,
Step (1) : we take the value of 1 variable from 1 equation ,
Step(2) : we substitute the value of that variable in equation(2) and solve to get the solutions .
let us understand the method of substitution with the help of example .
Let the 2x2 linear system be 2x + 3y = 14 and x + y = 12
From , x+y=12 , we get
x = 12 - y ,
Substituting the value of x in 2x + 3y = 14 ,
we get ,
2(12 - y) + 3y = 14
So , y = -10
putting in x = 12 - y ,
we get ,
x = 12-(-10) = 22 .
Therefore , the method to solve the 2x2 linear system is explained .
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6. Annie orders a coke for $1.75, pasta primavera for $14.50, and ice cream for $3.25 when out to dinner with friends. If the tax rate is 8.25%, and Annie plans to leave a 17% gratuity, what will be the total cost for her meal?
Answer:
Step-by-step explanation:
1.75+ 14.50+ 3.25= 19.5
8.25% of 19.5= 1.60875
19.5 + 1.60875= 19.7 rounded
19.7+ 17%= 19.87
$19.87 is the total
I rounded so the closest to this might be the answer
which of the correlation values represent a perfect linear relationship between x and y? A. 0,5 B. 100 C. 1 D. -1 E. 0
The correlation coefficient that represents a perfect linear relationship between x and y is 1 and -1. (Option C and D)
The correlation coefficient refers to a statistical measure of the strength of a linear relationship between two variables and lies with the range from -1 to 1. In other words, a correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another.
A linear relationship is a statistical term which is used to describe a straight-line relationship between two variables. A perfect linear relationship refers to a relationship in which one of the variables can be perfectly explained by a linear function of the other and can be achieved by the correlation coefficient of 1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
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I need help please! Describe how the graph of g(x) is related to graph of f(x) = x³.
a. g(x) = (x-4)³
b. g(x) = -5x³
Answer:
Step-by Graph the line using the slope and y-intercept, or two points
Slope=3
y-intercept=18-step explanation:
How do you use the sine rule to work out an obtuse angle?
The value of the obtuse angle by applying sine rule for the attached diagram is equal to x° = 38.2°.
As given in the question,
Diagram of the obtuse angle triangle is attached.
In the given triangle,
Name the vertex of angle x as 'C' and side opposite to angle x as AB.
Draw a perpendicular from point A to BC at point D such that AD = z .
Given m ∠ACB = x°
AB = 2y
AC = y
m ∠ABC = 18°
In ΔADB,
sinB = AD / AB
⇒ sin 18° = z / 2y __(1)
In ΔACD,
sin ACD = AD / AC
⇒ sin ( 180 - x )° = z / y __(2)
Divide (1) by (2) we get,
sin18° / sin ( 180 - x )° = ( z / 2y ) / ( z / y )
⇒ sin 18° / sinx° = 1 / 2
⇒ sinx° = 2sin18°
⇒ sinx° = 2 (0.309 )
⇒ x° = sin⁻¹( 0.618)
⇒x° = 38.2°
Therefore, the obtuse angle for the given attached diagram using sine rule is equal to 38.2°.
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before i can open my gym locker, i must remember the combination. two of the numbers of this three-term sequence are 17 and 24, but i have forgotten the third, and do not know which is which. there are 40 possibilities for the third number. at ten seconds per try, at most how long will it take me to test every possibility? the answer is not 40 minutes!
Therefore, 6 minutes and 40 seconds are needed to test possibilities.
Describe combination.Combinations are sometimes known as selections. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. To denote the number of unique r-selections or combinations among a set of n items, we write n C r. Combinations are distinct from arrangements or permutations.
Here,
The first two numbers in this three-term series are 17 and 24, and the third one remains a mystery.
Given that there are 40 options for the third number and that each try takes 10 seconds, we have 40 x 10 seconds, or 400 seconds, to try every possible combination.
Thus,
=> 400 seconds is equals to 6 minutes and 40 seconds
Therefore, 6 minutes and 40 seconds are needed to test every scenario.
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the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
The length of the perimeter of the rectangle = 112 cm or 44 inches
Given in the question,
Area = [tex]105in^{2}[/tex]
= 677.4 [tex]cm^{2}[/tex]
Length of one side of the rectangle = 7 inches
= 17.7 cm
∴ Since the length of one side of the rectangle is given in the question we need to find the width of the rectangle to calculate the total perimeter of the rectangle
⇒ Area = length x width
⇒ 677.4 = 17.7 x width
⇒ Width = [tex]\frac{Area}{Length}[/tex]
⇒ Width = [tex]\frac{677.4}{17.7}[/tex]
⇒ Width = 38.2 cm
As we got both the length and the width of the rectangle, now we can calculate the perimeter,
⇒ Perimeter = [tex]2( length + width)[/tex]
⇒ Perimeter = [tex]2(17.7 + 38.3)[/tex]
⇒ Perimeter = 2 x 56 cm
⇒ Perimeter = 112 cm
⇒ In inches = 44 inches
Therefore, the length of the perimeter is = 112cm or 44 inches
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Solve using elimination.
4× - 3y = -8
9x - 3y = 12
Step-by-step explanation:
Simulteanous EquationsSimulteanous Equations are multiple equations with corresponding number of unknown variables.
They can be solved by 2 methods: Substitution and Elimination Method.
Solutionx = 4
y = 8
We will use the Elimination Method since the question specify as so.
4x - 3y = -8 (Equation 1)
9x - 3y = 12 (Equation 2)
By using Equation 1 - Equation 2,
4x - 9x - 3y - (-3y) = - 8 - 12
-5x - 3y + 3y = - 20
-5x = - 20
x = - 20 ÷ - 5 = 4
Now we substitute x = 4 into Equation 1.
4(4) - 3y = - 8
16 - 3y = - 8
-3y = - 8 - 16
-3y = - 24
y = - 24 ÷ - 3
= 8
Therefore the varables are:
x = 4
y = 8
11. there are two statements: 1. there are 45 students in class. 2. 12 students scored less than mark. which statements are needed to find the rank of mark? both 1 and 2 need 3rd statement only 1 only 2
To find rank of mark
From the given options 1st option is correct
both 1 and 2 need
Given statements are
1. there are 45 students in class.
2. 12 students scored less than mark.
we need both 1 and 2 statements to find the rank of mark
without knowing the class strength we cannot find the rank of marks
and we should also know that how many students have scored less than mark in 2nd statement it is given that 12 students scored less than mark.
from the given options 1st option is correct
both 1 and 2 need
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Tabitha planted an evergreen tree in her front yard. It was 12 feet tall. The next year it was 20% taller. How much taller, in feet, was the evergreen tree in Tabitha’s yard?
The evergreen tree grew 2.4 feet taller the next year.
What are Percentages?Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
It is given by:
Percentage = (given value / total value) * 100%
From the question, the tree has a base height of 20m, if it grew 20% taller then;
tree height = 12 x (20/100)
tree height = 12 x 0.2
tree height = 2.4
Therefore, the tree grew 2.4 feet taller the next year.
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passes through (2,3) and is parallel to y=1/2x-1
Answer:
y = [tex]\frac{1}{2}[/tex]x + 2
Step-by-step explanation:
Parallel lines have the same gradient, so
y = [tex]\frac{1}{2}[/tex]x + c
Put in your point (2,3):
(3) = [tex]\frac{1}{2}[/tex](2) + c
3 = 1 + c
3 - 1 = c
2 = c
So
y = [tex]\frac{1}{2}[/tex]x + 2
8. A square has an area of 40 square feet. What is the length of a side of the square, in feet? PLEASE HELP I NEED IT ASAP
A
[tex] \sqrt[4]{10} [/tex]
B
[tex]10[/tex]
C
[tex]20[/tex]
D
[tex] \sqrt[2]{10} [/tex]
Answer:
The length of the side of the square should be 10ft
Step-by-step explanation:
Calculation of the length of the side:
Since A square has an area of 40 square feet.
As we know that the square does have 4 sides
So, the length of the side of the square should be
40 divided by 4
= 10ft
a group spends $277.50 to rent 15 tubes for a float down the ichetucknee river. how many of each type of tube does the group rent?
Answer: $18.50
Step-by-step explanation:
Take 277.50 divided by 15 = $18.50
The required price of each tube for rent is given as $18.6.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Renting 15 tubes for a float down the Ichetucknee River costs $277.50 for a group.
So,
Let the rent of each tube be x,
According to the question,
15x = 277.50
x = 277.50 / 15
x = 18.6
Thus, the required price of each tube for rent is given as $18.6.
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An unopened package of cream cheese contains
8
1
4
8
1
4
ounces of cream cheese. A serving is
3
4
3
4
of an ounce. What is the greatest number of servings that can be made from this package?
The greatest number of servings that can be made from this package is 11.
How to calculate the number of ounce?This can be illustrated through an expression. Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
Since the unopened package of cream cheese contains 8 1/4 ounces of cream cheese and a serving is 3/4 of an ounce.
The greatest number of servings that can be made from this package will be simply be gotten by dividing the fractions that are given in the question. In this case this implies that we have to divide 8 1/4 by 3/4. This will be illustrated as:
= 8 1/4 ÷ 3/4.
= 11
The above calculation simply shows that the greatest number of serving will be 11.
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what is the null hypothesis of the dickey-fuller test 1? the series is stationary around a 0 mean the series is stationary around a non 0 mean the series is non-stationary and has 0 mean the series is non-stationary and has a non 0 mean
If you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.
What is Null hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Consider the given process:
[tex]x_{t} = c+\alpha x_{t-1}+\beta _{t} \\E[\beta _{t}]=0\\[/tex]
Obtain mean,
[tex]E[x _{t}]=\frac{c}{1-\alpha }[/tex]
This works only when |α|<1. If α=1 this doesn't work, it blows up, because , [tex]E[x _{t}]\neq E[x _{t-1}][/tex] i.e. the process is not stationary.
The constant refers to the term c.
The trend is easy too:
[tex]x_{t} +c+\alpha t+\alpha x_{t-1} +\beta_{t}[/tex]
In this case,
[tex]E[x _{t}]=\frac{c+\alpha t}{1-\alpha }[/tex]
So, if you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.
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Find KL in the image below
By Midsegment theorem we find the length of KL is 8.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We know by midsegment theorem, the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
The length of midsegment KL =1/2 of the length of the third segment FH.
KL = 1/2(FH)
KL = 1/2(16)
KL is sixteen divided by 2.
KL = 8
Hence, the length of KL is 8.
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I need help:/
………………
Using system of linear equations, the number of students in year book is 25 and that of film making are 39
System of Linear EquationSystem of linear equations can be defined as the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
Using variables x and y to represent to unknown values;
x = number of students in film makingy = number of students in year bookx + y = 64 ...eq(i)
x = 14 + y ...eq(ii)
Put eq(iii) into eq(i)
14 + y + y = 64
14 + 2y = 64
2y = 64 - 14
2y = 50
y = 25
Put y = 25 into eq(ii)
x = 14 + 25
x = 39
The number of students in film making is 39 and year book is 25
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The legs of a right triangle are congruent and have the measure of 23.6 yards. Determine the length, in yards, of the hypotenuse. Show your work for partial credit.
The length is 33.37 yards of the hypotenuse.
What is Congruence of triangles ?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In congruent triangle, corresponding sides are equal.
We know, Pythagorean theorem is
Hypotenuse ² = perpendicular² + base²
Let x = be the measure of length of two legs of a right triangle
H² = x² + x²
H² = 2x²
We know, x = 23.6 yards
H² = 2(23.6)²
H² = 1113.92
H = 33.37 yards
Hence, the length is 33.37 yards of the hypotenuse.
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What is something about periodic table and atoms
The periodic table is useful for understanding atomic properties that show periodic trends. Periodic trends are specific patterns that are present in the periodic table that illustrate different aspects of a certain element, including its size and its electronic properties.
Find f(3)-(5) given f(x) = 8(.5) and gix) = 2x+1
Answer:
Hope it helps
Step-by-step explanation:
f(3)-g(5) = 8(.5) - (2(5)+1) = 4 - 11 = -7
the margin of error of a confidence interval is the error from biased sampling methods. True or False
It is false, that the margin of error of a confidence interval is the error from biased sampling methods.
The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.
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a 5.0L v8 pickup truck takes 7.7 quarts of oil with a tolerance of 0.2 quarts. Write an equation representing the minimum and maximum fill capacity tolerated by this truck.
Answer:
Step-by-step explanation:
cdcdfcdfvdsfdf
one hundred eighty patients were treated for disease x from 2007 to 2009, and their progress was followed to 2010. the treatment results are given in the table. no patients were lost to follow-up. what is the probability of surviving for 3 years?
The probability of surviving for 3 years will be 54.8.
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.
Given:
one hundred eighty patients were treated for disease x from 2007 to 2009.
The probability of surviving for 3 years=P 2007*P 2009*P 2010.
According to given information,
The probability of surviving for 3 years will be 54.8.
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