The potential outliers, given the normal annual precipitation in the different U.S. cities are E. 59.4; 65.3.
What are outliers?Outliers in a data distribution are values or data points that are far from the other points in the data. These can be statistically significant when they distort measures of central tendency such as mean.
In this case, the potential outliers in the normal annual precipitation 59.4 and 65.3 because they are far from the highest annual precipitation (before them) of 47.2 inches. 9.2 inches is quite low but it is close to 12.3 inches and 13.6 inches and so is not an outlier.
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Identify the values of the variables. Give your answers in simplest radical form. Help!
Considering the triangle given the variables are calculated to be
x = (5√6)/3
y = (10√6) / 3
How to calculate the unknown variablesInformation given in the question
right angle triangle
The unknown variables is calculated using SOH CAH TOA
Definition of variables for the right angle triangle
hypotenuse = y
opposite = 5√2
adjacent = x
The variable x is solved using tan, TOA, the angle is 60
tan 60 = Opposite / Adjacent
tan 60 = (5√2) / x
x = (5√2) / tan 60
x = (5√6)/3
The variable y is solved using sin, SOH, the angle is 60
sin 60 = Opposite / Hypotenuse
sin 60 = (5√2) / y
y = (5√2) / sin 60
y = (10√6) / 3
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The coordinates of the endpoints of
KL
are K(
–
16,10) and L(
–
9,
–
11). Point M is on
KL
and divides it such that KM:LM is 4:3.
What are the coordinates of M?
Write your answers as integers or decimals.
The coordinates M along the directed line segment is (-12, -2)
How to find the coordinates of the point along the directed line segment?The points are given as:
K = (-16, 10)
L = (-9, -11)
The ratio on the segment can be represented as;
KM : LM, m : n = 4 : 3
So, we have the coordinates of the point M that lies along the directed line segment to be
M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
So, we have:
M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)
Evaluate
M = 1/7 * (-84, -14)
Evaluate
M = (-12, -2)
Hence, the coordinates of the point M is (-12, -2)
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6 sqrt 44z + sqrt 99z
Answer: 15√11z
Step-by-step explanation:
Name a plane in the image.
A
•C
B
Answer:
ABCStep-by-step explanation:
A is a point
AB is a line
ABC is a plane
Therefore, ABC is a plane.
__________________
Hope this helps!
Have a great day!
or
The equation of line k is y=
–
10x–8. Perpendicular to line k is line , which passes through the point (2,2). What is the equation of line ?
Considering the definition of perpendicular line, the equation of perpendicular line is y= -1/10x + 11/5.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 10x -8.
The line has a slope of 10. If you multiply the slopes of two perpendicular lines, you get –1:
10× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 10
slope perpendicular line= -1/10
The perpendicular line has a form of: y= -1/10x + b
The line passes through the point (2, 2). Then:
2= -1/10× (2) + b
2= -1/5+ b
2+ 1/5= b
11/5= b
Finally, the perpendicular line is y= -1/10x + 11/5.
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2(4 - 2w) - 8 = -4
w = ?
Use the distributive property to multiply 2 times 4−2w.
8 - 4w - 8 = -4Subtract 8 from 8 to get 0.
-4w = -4Divide both sides by −4.
w = -4/-4Divide −4 by −4 to get 1.
w = 1Answer:
w = 1
Step-by-step explanation:
2(4 - 2w) - 8 = -4
(2*4 + 2*-2w) - 8 = -4
(8 - 4w) - 8 = -4
-4w + 8 - 8 = -4
-4w = -4
w = -4/-4
w = 1
Check:
2(4 - 2*1) - 8 = -4
2(4-2) -8 = -4
2(2) - 8 = -4
4 - 8 = -4
Alyssa is signing up for a gym membership with a one-time fee to join and
then a monthly fee to remain a member. Let C represent the total cost of the
gym membership over t months. The table below has select values showing
the linear relationship between t and C. Determine the one-time joining fee.
Answer: $
t
2
4
9
C
200
250
375
Submit Answer
The one time joining fee found from the linear relationship between total cost and the number of months of membership is $250
What is a linear relationship?A linear relationship is a relationship between two variables that has a straight line when graphed.
The total cost of the gym membership = C
The number of months of membership = t
The table in the question is presented as follows;
t (Time in months) [tex]{}[/tex] C (Total cost)
2 [tex]{}[/tex] 200
4 [tex]{}[/tex] 250
9 [tex]{}[/tex] 375
The linear equation that represents the value in the table is found as follows;
Slope of the line, m = (375 - 250)/(9 - 4) = 25
The equation of the line in point and slope form is therefore;
(C - 375) = 25·(t - 9)
C = 25·(t - 9) + 375
C = 25·t - 225 + 375 = 25·t + 250
C = 25·t + 250
The joining fee is the amount paid at the start when t = 0, therefore;
Joining fee = 25 × 0 + 250 = 250
The one time joining fee is $250
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(2 points) Let x³ - 2x²-x+2=0 be a polynomial equation. Find the list of all potential rational solution(s) for the polynomial equation using the
Rational Root Theorem. Then, find the actual rational solution(s).
1. Find all potential rational solution(s).
Answer (separate by commas):
2. Find all distinct actual rational solution(s).
Answer (separate by commas):
Note: You can earn partial credit on this pmblem
Potential rational solution(s) to the above polynomial equation is ±1, ±2.
Actual rational solution are ±1, +2.
What is polynomial equation?
Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.
Main Body:
Given:
x³ - 2x² - x +2 = 0
We will use the Rational Root Theorem:
If the rational number r/s is a root of a polynomial whose coefficients are integers, then the integer r is a factor of the constant term, and the integer s is a factor of the leading coefficient.
So, if the constant therm is 2 and the leading factor is 1, candidates for roots are:
±1,±2
Dividing x³ - 2x² - x +2 = 0 by x-1, we get
x²-x-2 as quotient.
Splitting the middle term ,
⇒x² - 2x + x - 2
⇒x(x- 2) + 1(x-2)
⇒(x+1)(x-2)
so x= -1 , 2
Hence the rational solution to the equation are ±1, 2.
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there are 4 consecutive even integers that sum to 276
The required consecutive even integers are 66, 68, 70, and 72.
We have four integers. The integers are consecutive, that means the integers are one after the other. The integers are even, which means they are all divisible by two. The sum of these four even integers is 276.
Let the first even integer be represented by the variable "n". The next three consecutive integers are (n + 2), (n + 4), and (n + 6). Let the sum be denoted by "S".
S = n + (n + 2) + (n + 4) + (n + 6)
276 = 4n + 12
4n = 264
n = 66
Hence, the required integers are 66, 68, 70, and 72.
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What is the end behavior of the graph?
Responses
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches negative infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity., , ,
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches negative infinity.
The end of the graph is
As x approaches infinity, f open argument x close argument approaches negative infinity., , As x approaches negative infinity, f open argument x close argument approaches infinity
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to ∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionThis is determined by examining the graph and the coordinates.
The graph shows as at the positive side of the x coordinate, as x tends to ∞ the curve is pointing down - ∞The graph shows as at the negative side of the x coordinate as x tends to - ∞ the curve is pointing up ∞The end behavior is can be written as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ ∞
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The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Derek's hourly rate is $10 and Charlie's hourly rate is $10.45, Charlie's earns $0.45 more per hour than Derek.
What is unit rate?A unit rate means a rate for one of something.
Given that, a graph which shows Derek's earning hourly, and Charlie earns $52.25 in 5 hours of work,
Derek's earns $10 for an hour
Charlie's earning for an hour = 52.25/ 5 = $10.45
Hence, Charlie's hourly rate is $10.45, and he earns $0.45 more per hour than Derek.
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The effect of the time of day a science class is laught on test scores is being studied in an experiment. Giving every student in the experiment the same final exam is an example of which experimental design principle?
Giving every student in the experiment the same final exam is an example of A. Randomization.
What is an experimental design?The process of conducting research in an objective and controlled manner in order to maximize precision and draw specific conclusions about a hypothesis statement is known as experimental design.
The process in which participants in clinical trials are randomly assigned to separate groups that receive different treatments or other interventions. Neither the researcher nor the participant has any say in which treatment or intervention the participant receives.
A random process is a sequence of random variables that describe a process whose outcomes follow an evolution described by probability distributions. This was illustrated in the examination.
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Complete options
A. Randomization
B. Blocking
C. Direct control
D. Replication
Determine the value of each expression. |-2-8|-|−5|
Answer:
5
Step-by-step explanation:
:)
Answer:5
Step-by-step explanation:|-10|-|-5|
10-5
5
A quarterback threw a football from a height of 6 feet with an initial velocity of 20 feet per second. The height, h, of the ball at time t seconds can be represented by
the equation h (t)=-16t² + 20t+6.
True or False?
The ball was in the air for 1.5 seconds before hitting the ground.
The ball was in the air for 1.5 seconds. The answer is true.
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
The given equation is h(t) = -16t² + 20t + 6.
To find the time for which the ball was in the air, substitute h(t) =0.
0 = -16t² + 20t + 6
Use the quadratic formula to solve the equation:
[tex]t= \frac{- 20 \pm\sqrt{20^2 - 4(-16)(6)}}{2(-16)}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{400+384}}{-32}\\t=\frac{- 20 \pm\sqrt{784}}{-32}\\\\t= \frac{- 20 \pm28}{-32}[/tex]
t = (-20 + 28)/(-32) or t = (-20-28)/(-32)
t = -0.25 or t = 1.5
Since time cannot be negative, discard the negative value.
Hence, the ball was in the air for 1.5 seconds. The answer is true.
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A letter is chosen at random from the word MATHEMATICS. Find the probability that it will be
a) an H
b) an M
c) a B
d) a vowel,
e) a letter other than an A
Answer:
a) 1/11
b) 2/11
c) 0/11
d) 4/11
e) 9/11
Step-by-step explanation:
'MATHEMATICS' has 11 letters.
a) there is only one H out of the 11 letters meaning the probability is 1/11
b) there are two M s out of the 11 letters meaning the probability is 2/11
c) there is no B in the word meaning the probability is 0/11
d) there are four vowels (2 A s, 1 E and 1 I) out of the 11 letters meaning the probability is 4/11
e) there two A s in the word and 11-2=9 meaning the probability is 9/11
Hope this helps :)
A house on the market was valued at $355,000 . After several years, the value decreased by 9%. By how much did the house's value decrease in dollars? What is the current value of the house?
Answer: $323,050
Step-by-step explanation:
355,000 over 1 x 9 over 100 = 3195000 over 100 (31950)
355,000- 31,950 = 323,050 which is your answer, hope this helped <3
Graph The any form equation 3(-2x-4y-3) = 5(x - 5y + 10) Build equation with the given information (2) slope = m = -5 point (-3,-2) 3 point 1 (-5,-3) point2 (-7,-9) Build an equation parallel to the given equation and passing through The point 47 y = - ³²/²x-4 point (-7,5)
Here is what i did
I used a graphing calculator
If Ø (theta) is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec Ø (theta) in simplest radical form.
For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.
As given in the question,
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( -9, 5 )
( -9 , 5 ) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = -9
Altitude = 5
Using Pythagoras theorem,
Hypotenuse² = (-9)² + (5)²
⇒ Hypotenuse = √106
cos ∅ = -9 / √106
sec ∅ = 1/ cos ∅
= - √106/9 ( simplest radical form )
Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of
sec∅= ( - √106/ 9 ) in simplest radical form.
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find the value of the ratio (red to blue) of the areas of the similar figures. Write the ratio as a fraction in simplest form. 12 and 8
The ratio of the areas of the similar figures is given as follows:
225/16.
What are similar figures?Similar figures are figures that share these two features:
Congruent angle measures, that is, the same angle measures.Proportional side lengths.The ratio of the side lengths of the similar figures can be represented as follows:
(b/a).
The side length is measured in units, while the area is measured in units squared, hence the ratio of the areas of the similar figures is represented as follows:
(b/a)² = b²/a².
From the image of the right triangle shown at the end of the answer, the ratio of the side lengths is:
15/4.
Hence the ratio of the areas of the figures is given as follows:
(15/4)² = 225/16.
Missing InformationThe figures are given by the image at the end of the answer.
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The daily production costs for a golf ball manufacturer can be modeled with the function C(x) = 0.1x2 - 7x + 140, where C(x) is the total cost and x is the number of golf balls produced per hour. Use the graph to answer the question.
Graph of function c of x equals 0 point 1 x squared minus 7 x plus 140. The graph has the axis labeled as number of golf balls produced, and the y-axis labeled as cost. The curve begins at (0, 140), decreases to (35, 17.5), and then increases to infinity.
Which statement shows the correct relationship between production cost and number of golf balls produced?
The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Then the minimum is represented by the formula;
c - b² / 4a
We have given equation C(x) = 0.1x² - 7x + 140
a = 0.1
b = -7
c = 140
Now plugging in values to c - b² / 2a
= 140 - 7² / (4 * 0.1)
= 17.5
The minimum production cost will be; 17.5
Now plugging 35 into the given equation;
C(x) = 0.1x² - 7x + 140
C(x) = 0.1 ( 35)² - 7 (35) + 140
C(x) = 17.5
Therefore, 35 golf balls produce the minimum cost.
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Answer:
that the minimum production cost of 17.5 occurs when 35 golf balls are produced.
Step-by-step explanation:
Graph the line with slope 1 passing through the point (-2 , -5)
Graph the line.
The equation of the line is y = x -3. The graph of the line is attached below.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
Given that the slope of the line is 1.
Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.
Putting m = 1 in y = mx +c:
y = 1 × x +c
y = x +c
Since the line passes through the point (-2, -5), thus the point satisfies the given equation of line.
Putting x = -2 and y = -5 in y = x +c
-5 = -2 + c
c = -3
The equation of line is y = x - 3.
The points on the line are
(-2, -5), (0, -3), (3, 0).
Plot the points and join them:
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Warren likes to draw pictures of people and animals. In his notepad, he has drawn 2 pictures of people for every 5 pictures of animals.
If Warren has drawn 18 more pictures of animals than people in his notepad, how many pictures of animals has he drawn
By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Warren has drawn 5x pictures of animals and 2x pictures of people
Warren has drawn 18 more pictures of animals than people in his notepad
By the problem,
5x - 2x = 18
3x = 18
x = [tex]\frac{18}{3}[/tex]
x = 6
Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]
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What is the slope of the line that passes through the points (-6, -7) and (-3, -2)?
Simon bought a $48 table on sale at 30% off.
Select from the drop-down menu to correctly complete the sentence
0.03(50)
0.3(50)
3(50)
30(50).
Simon bought a $48 table on sale. The price of the table can be estimated by $50.
The sale propose 30% off, then an estimate for the discount can be calculated using proportion:
$50 -- 100%,
$x -- 30%
that is mathematically
Find x:
Answer: correct choice is B
Determine the interval(s) on which the function is (strictly) increasing.
Write your answer as an interval or list of intervals.
When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None" if applicable.
Answer:1341
Step-by-step explanation:
1342123
mass
density
volume
2.23 kg of oxygen gas has a volume of 1.56 x 106 cm³.
Calculate the density of the oxygen gas in g/cm³.
Give your answer in standard form to 3 significant figures.
Answer:
density = 1.43 × 10⁻³ g/cm³
Step-by-step explanation:
We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.
To do this we have to first convert the mass, which is given in kg, to g:
mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]
= 2230 g
Next, we can find the density of the gas using the following formula:
[tex]\boxed{density = \frac{mass}{volume}}[/tex]
⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]
= 1.43 × 10⁻³ g/cm³
Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.
Pls help question 9 and 10
The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.
AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.
In the given figure FE║GE means FE is parallel to GE.
so ∠EFS = ∠HGS
and ∠FES = ∠GHS
also ∠S is common for both.
If two triangles are similar then ratio of corresponding sides are also same.
So, by applying this
[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]
54/24 = FE/20
( 54*20 ) / 24 = FE
FE = 45m.
Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.
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why is not inverse function??
[tex]f(x) = x {}^{2} - 9[/tex]
The equation formed when x is the subject of the function f(x) = x² - 9, has two values of output for each input value to the function, therefore;
f(x) = x² - 9 does not have an inverse.
What is the inverse of a function?An inverse of a function is an anti function that reverses the values in the output into the input values thereby undoing the operations performed by the function.
A function f has an inverse if and only if it is bijective, such that there is a one to one correspondence between the set of the input elements and the set of the output elements
A function that has an inverse is said to be a bijective or invertible function or a function with one-to-one correspondence
The function in the question f(x) = x² - 9
Making x the subject of the function to verify if it has an inverse gives;
x² = f(x) + 9
[tex]x = \pm\sqrt{f(x) +9}[/tex]
Putting x = f⁻¹(x) gives;
[tex]f^{-1}(x) = \pm\sqrt{x +9}[/tex]
Therefore, each value of x gives two values of f⁻¹(x), such that the set of the output of inverse function, f⁻¹(x) does not have a one-to-one correspondence with the set of values of x.
The function f(x) = x² - 9 is not invertible and therefore does not have an inverse function.
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manuel wishes to purchase 25cent and 30 cent stamps. he decides to buy 10 fewer 30 cent stamps. How many of each can he buy for no more than $19.00
Using the simplification, Manuel buy 15 stamps of 25 cents and 5 stamps of 30 cent.
In the given question,
Manuel wishes to purchase 25 cent and 30 cent stamps.
He decides to buy 10 fewer 30 cent stamps.
We have to find how many of each can he buy for no more than $19.00.
Let he buy x stamps of 25 cent.
He want to buy 10 fewer 30 cent stamps.
So he buy x−10 stamps of 30 cent.
But he have to buy total stamps of $19.
So the equation is
x+x−10 = 19
Simplifying
2x−10=19
Add 10 on both side
2x−10+10=19+10
2x=29
Divide by 2 on both side
2/2 x =29/2
x=14.5
x≈15
Hence, he buy 15 stamps of 25 cent.
Now finding the number of 30 cent.
he buy x−10 stamps of 30 cent.
So 15−10=5.
So he buy 5 stamps of 30 cent.
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how to find perimeter of a triangle?
Answer:
Just add the 3 sides together
Step-by-step explanation:
if a triangle has the side values of 3, 4, 6. Then you would simply add them together!
3+4+6=13
therefor that triangles perimeter is 13
hope this helps!