The z-score is -0.428
What is a z-score?A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.
You can plot a z-score on a normal distribution curve.
You must be aware of the mean and population standard deviation to use a z-score.
Z-scores allow results to be compared to a "normal" population.
According to the question,
x=500
μ=533
σ=77
z-score=(x-μ)/σ
On substituting the values,
z-score=(500-533)/77
= -0.428
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Calculate the area of triangle abc with altitude bd, given a (-6,0) b (0,0) c (o,6) and d (3,-3)
The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).
We are required to find the area of the triangle when bd is the altitude of the triangle.
When we draw the triangle we will find that that the base is ac and altitude is given bd.
ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36+36}[/tex]
=[tex]\sqrt{72}[/tex]
=6[tex]\sqrt{2}[/tex]
bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]
=[tex]\sqrt{9+9}[/tex]
=[tex]\sqrt{18}[/tex]
=3[tex]\sqrt{2}[/tex]
Area=(Base*Height)/2
=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2
=(18*2)/2
=18 square units.
Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
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An equilateral triangle has a median drawn from one angle to the opposite side. What is the measure of each angle formed by the place where the median meets the vertex?
(Step by step pls)
Worth 20 points
The measure of each angle formed by the place where the median meets the vertex is 30 degrees
How to determine the angle?The median of an equilateral triangle divides the side and the angle into equal parts.
If the angle at the vertex is, the new angle would be
Angle = x/2
The angle at the vertex of an equilateral triangle is 60.
So, we have:
Angle = 60/2
Evaluate
Angle = 30
Hence, the measure of each angle formed by the place where the median meets the vertex is 30 degrees
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PLEASE I NEED HELP ASAP
The question is :
Danielle reflects shape S in the line x = - 1 , and then reflects the new shape in the line y = 2
Zachary reflects shape S in the line y = 2 , and then reflects the new shape in the line x = - 1
Work out the coordinates of the vertex that A maps to after
a) Danielle's two reflections.
b) Zachary's two reflections.
.
The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
How to determine the coordinates of the vertex that A maps to after the two reflections?From the given figure, the coordinate of the vertex A is represented as:
A = (-5, 2)
The coordinates of the vertex that A maps to after Daniel's reflections
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A' = (5 - 2, 2)
Evaluate the difference
A' = (3, 2)
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A'' = (3, -2 + 4)
Evaluate the difference
A'' = (3, 4)
Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)
The coordinates of the vertex that A maps to after Zachary's reflections
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A' = (-5, -2 + 4)
Evaluate the difference
A' = (-5, 2)
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A'' = (5 - 2, 2)
Evaluate the difference
A'' = (3, 2)
Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
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The taxi fare for the first two miles is $5 and for each additional mile the fare increases by $ 2. What is the taxi fare for a journey of n miles in dollars?
The taxi fare for a journey of n miles in dollars is 1 + 2n
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the equation of the system?The given parameters about the taxi fares are given as
First two miles = $5
Additional mile = Increment of $2
Let the number of miles be n
So, we have:
2 miles = $5
Additional miles = (n - 2) * 2
Add the above expressions
5 + (n - 2)* 2
Represent the value with f(n)
So, we have:
f(n) = 5 + (n - 2)* 2
Expand the bracket
f(n) = 5 + 2n - 4
Collect the like terms
f(n) = 5 - 4+ 2n
Evaluate the like terns
f(n) = 1 + 2n
Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n
So, the complete parameters are:
First two miles = $5
Additional mile = Increment of $2
n miles 1 + 2n
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If a union member does not pay their union dues, they will not be able to
Answer:
The ¨mandatory dues¨ asked by the unions are not much (practically none), since it´s a voluntary system implemented, normally all the members pay a ¨agency fee¨ but not more than that, this changes depending on the personal involvement with the union.
a natural person can refuse the membership at any moment, without issues, and this way avoid any kind of activity with the union, including contributing with money (dues) or duties.
However, when this happens, the person it´s restricted to certain activities like participate in union elections, general or important meetings, and the contribution in the bargain for the collective elections is banned as well, these as main aspects to highlight.
If one doesn't pay they union dues, they will not be able to participate in collective bargaining with owners.
Only the real representatives of the union could participate in collective bargaining with owner (in which they could negotiate the new term of the salary with the owner). Without paying their dues, they're still haven't been acknowledged as the member of union.
Hope this helps have a great day!
In a survey of 1002 people, 701 (which is 70%) said that they voted in the most recent presidentia l election (based on data from ICR Research Group). The margin of error for the survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this necessarily imply
Based on the percentage of people who actually voted and the margin of error, the data implies that people lied when responding to the survey.
What is the evidence that people lied?The evidence that people lied about voting would bet be shown by the confidence interval. If the confidence interval of the survey does not have the actual percentage of people who voted in it, then people lied.
The confidence interval is:
= Average ± Margin of error
Solving:
= 70% + 3%
= 73%
= 70% - 3%
= 67%
Confidence interval is:
67% - 73%
The actual percentage of 61% who voted is not in this interval which means that some people lied about voting in the survey.
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Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside.
How high does the center of the frame need to be?
The height of the frame is 15 feet.
How to calculate the height?From the information given, the following can be depicted:
b - 10/a = 2/5
2a = 5b - 50
2a - 5b = -50
Also, slope of AC:
= (b - 10(/(a - 5) = 2/5
2a - 50 = -5b + 50
2a + 5b = 100
Both equations will be solved
The height of the frame will be:
= 5 + 10
= 15 feet
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What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
Answer:
Greetings!A) Domain: x∈R or in interval notation (- ∞, ∞)
Range: x∈R or in interval notation (- ∞, ∞)
Thus, they both the domain & the range of the first function are the same.
B) Domain: x∈R or in interval notation (- ∞, ∞)
Range: [-5,∞)
Using it's concepts, the domain and the range of the functions are given as follows:
a) Both all real numbers.
b) Domain all real numbers, range [tex]y \geq 5[/tex].
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].
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help
Solve for x in the diagram below.
Answer:
X=10
Step-by-step explanation:
You can subtract 180 by 110 to get 70. Then you can do 8x+30+70=180
Add 30+70 to get 100
Subtract 100 to 180 to get 80.
8x=80
You divide 8 from both sides which leaves you with x=10.
Answer:
x=10
Step-by-step explanation:
See attached image
Find angle V
(2x +29)= (10x-27)
Answer:
137
Step-by-step explanation:
VYXW is a parallelogram.
The opposite angles of a parallelogram are congruent, meaning their angle measurements are equal.
Following this information we can write an equation to find the value of x:
10x - 27 = 2x + 29 transfer like terms to the same side of the equation
10x - 2x = 29 + 27 add/subtract
8x = 56 divide both sides by 8
x = 7 replace x with 7 to find the given angle measures
now, the consecutive angles in a parallelogram are supplementary meaning their sum is equal to 180
m<V + m<W = 180
m<V + 2*7 + 29 = 180
m<V + 43 = 180 subtract 43 from both sides
m<V = 137
This map of china is 65inches from east to west and 68 from the north to south. if 1 inch is 50 miles, how large is the actual country?
The country is 3250 miles in distance from east to west, and 3400 miles from north to south.
Given Information
It is given that,
The distance of the country on map from east to west, l = 65 inches
The distance of the country on map from north to south, b = 68 inches
As per the given scaling of map, 1 inch = 50 miles
How large is the actual country?
Thus, the actual distance from east to west, L = l × 50 miles
L = 65 × 50 miles
L = 3250 miles
The actual distance from north to south, B = b × 50 miles
B = 68 × 50 miles
B = 3400 miles
Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.
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Solve for x: 12x^2 – 6 (a^2 + b^2)x + 3a^2b^2 = 0
Step-by-step explanation:
[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]
Using quadratic formula, we get
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]
Answer: x₁=6b², x₂=6a².
Step-by-step explanation:
[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]
What is the equation of the line parallel to the given line with an x-intercept of 4? y = x
line segment connecting the vertices of a hyperbola is called the ________ ________, and the midpoint of the line segment is the ________ of the hyperbola.
line segment connecting the vertices of a hyperbola is called the transverse axis and the midpoint of the line segment is the center of the hyperbola.
What is transverse axis and center of hyperbola ?
The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci lie on the line that contains the transverse axis. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints.
And The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect. Every hyperbola also has two asymptotes that pass through its center. As a hyperbola recedes from the center, its branches approach these asymptotes.
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A certain university recently calculated the number of days that its students took to complete their master's degrees. It took 100 of the students 800 days. In contrast, it took 150 of the students 600 days. What is the average number of days that these students took to complete their master's degrees? a) 620 days b) 680 days c) 700 days d) 720 days?
Answer:
c) 700
Step-by-step explanation:
Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.
For the graph y = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined
How to determine the slope?The equation is given as:
y = 1
A linear equation is represented as:
y = mx + c
Where:
m represents the slope
By comparison, we have:
m = 0
The slope of the parallel line is:
Slope = m
This gives
Slope = 0
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/0
Slope = undefined
Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined
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Homer mowed 5 lawns in his first month and increased the number he mows by two for each month following. Which of the following is the correct interpretation of the rate of change and the initial value?
The equation which represent the interpretation of the scenario is 5 + 2x
AlgebraNumber of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = xTotal laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)
= 5 + (2 × x)
= 5 + 2x
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Using the sine rule, calculate the length y. Give your answer to 2 s.f.
Answer:
y = 9.84 mm
Step-by-step explanation:
Sine rule:Law of sine:
[tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]
a = y
A = 31°
b = 17 mm
B = 117°
[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]
[tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]
-8+(3x)
3
2
=
5834
729
Find the missing values
Answer:
5
Step-by-step explanation:
5×(-4)=20
5×3=15
5×0.5=2.5
5×5=25
5×0=0
5×(-2)=-10
True or
False?
A binary predictor variable is tested for significance using a different test statistic than used for a quantitative predictor variable.
Answer:
it is False
Step-by-step explanation:
find the mean of 3,2,4,6,5,6,1,7,9,8,10
Answer:
[tex]5\frac{6}{11}[/tex]
Step-by-step explanation:
Number of Values = 11.
Mean = Sum of values / Number of Values
= [tex]\frac{3+2+4+6+5+6+1+7+9+8+10}{11} \\=\frac{61}{11} \\= 5\frac{6}{11}[/tex]
41. The Puuur Place builds customized cat trees for pet owners. The basic tree is $100 and each additional platform, perch, or toy costs $50. Meow Now also builds customized cat trees. Their basic cat tree starts at $50 and each additional piece costs $75.
[A] Write and solve a system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store.
[B] Solve this system of equations and show your work.
[C] Reggie wants to purchase a cat tree for his pets. Based on your work, explain which store would be cheaper depending on how many add-ons he wants to purchase.
The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;
y = 50x + 100 ------(eq 1)
y = 75x + 50 ------(eq 2)
How to Solve Simultaneous Equations?A) Let the total cost of the cat tree be y
Let each additional piece added be x.
Since basic tree is $100 and each additional platform costs $50, then we can say that;
y = 50x + 100 ------(eq 1)
Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;
y = 75x + 50 ------(eq 2)
B) Subtract eq 1 from eq 2 to gte;
25x - 50 = 0
25x = 50
x = 50/25
x = 2
y = 75(2) - 50
y = $100
C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.
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Which of the x-values are solutions to the following inequality? x < 100
help pls i need now
Answer:
A and B
Step-by-step explanation:
x < 100 means x is less than 100. Therefore, pick any x-values that are less than 100 which are x = 54 and x = 89.
Hence, A and B are the answer.
if m = 2 and n = 5 then find the value of 6m+5n
Answer:
37
Step-by-step explanation:
6m+5n
plug in your given values
6(2) + 5(5)
12+25
=37
Answer:
37
Step-by-step explanation:
6m + 5n
6*2 + 5*5 = 12 + 25
= 37
Juan had 4 candy bars for his 3 friends to share after lunch. But then, three other friends joined them. If Juan wants each friend to get the same amount, what part of a candy bar will each friend get?
Using proportions, it is found that the fraction of each candy bar that each friend will get is:
[tex]\frac{2}{3}[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the three friends that were there initially and the three that arrived later, 4 candy bars will be split between 6 friends, hence the fraction that each will get is:
[tex]\frac{4}{6} = \frac{2}{3}[/tex]
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please answer asap with a clear answer
The permutations is computed below.
How to illustrate the permutations?1. Evaluate 9P4
9P4 = 9!/(9 - 4)
= 9!/5!
= (9 × 8 × 7 × 6)
= 3024
2. How many ways can 5 students sit on a row of 15 chairs for a photograph?
= 15!(15 - 5)
= 15!/10!
= (15 × 14 × 13 × 12 × 11)
= 360360
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i need the answer to number 9
Answer:
502.5
Step-by-step explanation:
C = 24(12) + 5.50(39)
C = 288 + 214.5
C = $502.5
C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
Putting the other player's king in check is always a good move. true or false subject: chess
Putting the other player's king in check is always a good move. true
What is chess?The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended. At the equal time, a king in the test is usually forced to move.The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test. A player may additionally pass the king, seize the threatening piece, or block the check with some other piece. A king cannot look at the opposing king, considering this will vicinity the first king in check as well.
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