what is the z score of x=12 if it is two standard deviations to the right of the mean?
The value of the Z-score will be equal to 2.
What is Z-score?The z score indicates how many standard deviations your score is from the mean.
At the mean position, the standard deviation is 0 now the z score is the measure of the data which is how far from the mean. So the given data is at two standard deviations to the right of the mean so the Z-Score will be 2.
Therefore the value of the Z-score will be equal to 2.
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Solve algebraically
X+4=-2
Answer:
x=-6
Step-by-step explanation:
-6+4=-2
Give brainliest please
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds.
= – (x – 5)2 + 3
y = –3(x –6)2 + x + 1
2seconds
3seconds
4seconds
5seconds
To make sure the flip is in unison after 4 seconds should the flip occur, as given by option C: 4 seconds.
We have given that,
Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience.
What does synchronized motion mean?Synchronized motion is a motion of two or more system which goes in synchronization with each other.
For this case, the flip will occur such that both gymnasts are synchronized and the flip is in unison (simultaneous).
For that, we need the time(x) and the height (y) same.
Since the motion paths are:
[tex]y=-(x-5)^2+3[/tex]
[tex]y=-3(x-3)^2+x+1[/tex]
Therefore, we need to find the values of x for which the same y comes as output.
Let x = t be the time for which the height y is the same, then:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex] = height achieved by both gymnasts.
Solving it further:
[tex]-(t-5)^2+3=-3(t-3)^2+t+1[/tex]
t=4,t=1/2
Assuming they planned to do a flip after an integral number of time in seconds, the correct option is t = 4 seconds.
Thus, to make sure the flip is in unison after 4 seconds should the flip occur, as given by the option C: 4 seconds.
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Billy received a raise after his first year on the job to $45,000 from his initial salary of $42,400. What was his real raise stated as a percentage? Inflation averaged 2.4 percent for the year. Round your answer to two decimal places.
Billy get 5.9% raise after completing first year.
What is PERCENTAGE?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Here, Billy's initial salary = $ 42,500
After raise, salary become $ 45,000
Change in salary = Raised salary - Initial salary
= 45000 - 42500
= $ 2500
% Change = change / initial salary X 100
= 2500 / 42500 X 100
= 0.0589 X 100
≈ 5.9 %
Thus, Billy get 5.9% raise after completing first year.
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Assume that the random variable X is normally distributed with mean y = 60 and standard deviation a = 12. Find the 87th percentile for X
The 87th percentile is the value [tex]x_{0.87}[/tex] such that 87% of the distribution lies below [tex]X=x_{0.87}[/tex], i.e.
[tex]P(X \le x_{0.87}) = 0.87[/tex]
Transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex], then solve for [tex]x_{0.87}[/tex] using the inverse CDF of [tex]Z[/tex].
[tex]P(X\le x_{0.87}) = P\left(\dfrac{X-60}{12} \le \dfrac{x_{0.87}-60}{12}\right) = P\left(Z \le \dfrac{x_{0.87}-60}{12}\right) = 0.87[/tex]
[tex]\implies \dfrac{x_{0.87}-60}{12} = F_Z^{-1}(0.87) \approx 1.12369[/tex]
[tex]\implies \boxed{x_{0.87} \approx 73.5167}[/tex]
Joe is going to travel to dallas. he lives 320 miles away and can average 69 miles per hour. use an equation to represent the distance d from dallas in terms of h, the number of hours joe has traveled. a. d = 69h c. d = 320 69h b. d = 320 - 69h d. d = 320h 69
The equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.
The total distance that Joe needs to cover to travel to Dallas = 320 miles {As he lives 320 miles away from Dallas}.
The distance that Joe covers after traveling for h hours at an average speed of 69 miles per hour = 69h {as Distance = Speed*Time}
Therefore, the distance left to cover by Joe, that is the distance from Dallas d can be written as the difference between the total distance needed to be covered and the distance Joe already covered.
Thus the equation is d = 320 - 69h.
Thus, the equation for the distance d from Dallas, in terms of h, the number of hours Joe has traveled is d = 320 - 69h. Hence, option B is the right choice.
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3. A-line segment has endpoints A(–2, 3) and B(6, –1):
i) Outline your strategy for finding the equation of its perpendicular bisector. (3C)
ii) Carry out the strategy and find the equation of its perpendicular bisector. (3T)
The equation of the segments perpendicular bisector is; y = -¹/₂x + 2
How to find the equation of the perpendicular bisector?i) Since it is a perpendicular bisector, hence point M is the midpoint. Thus;
Midpoint (AB) = [(x₁ + x₂)/2], [(y₁ + y₂)/2] = (x_m, y_m)
Slope AB will be;
m₁ = ((x₁ - x₂)/(y₁ - y₂))
Slope of perpendicular bisector is;
m₂ = -1/m₁
Equation of perpendicular bisector is;
(y - y_m) = m₂(x - x_m)
ii) Midpoint (AB) = [(-2 + 6)/2], [(3 - 1)/2] = (2, 1)
Slope AB will be;
m₁ = ((6 + 2)/(-1 - 3)) = -2
m₂ = -1/-2 = 1/2
Equation of perpendicular bisector is;
(y - 1) = -¹/₂(x - 2)
y - 1 = -¹/₂x + 1
y = -¹/₂x + 2
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A $15 credit to revenue was posted as a $150 credit by what amount is the revenue account in error?
Answer: Multiple Choice $15 understated. $135 overstated. $135 understated. $150 understated. $150 overstated. 2.The numbering system used in a company's chart of accounts: Typically begins with income statement accounts.
Step-by-step explanation:
Help asap much appreciated
hellooo
Step-by-step explanation:
so sine is 0 and (-1/3 isnt gonna positive out on the other side no is positive so ur last answer E is it
1.) Which of the following is not equal to 6¹⁰?
a. 2¹⁰ + 3¹⁰
b. (6²)⁵
d. (2 x 3)¹⁰
c. 2¹⁰ x 3¹⁰
2.) What is 25 ½ ÷ ½ ?
a. 25
b. 51
c. 12 ¾
d. 25 ¼
Answer:
1) a
2) b
Step-by-step explanation:
1) Lets check all the options
a) Cannot be simplified
b) [tex](6^2)^5=6^{10}[/tex] because [tex](a^m)^n=a^{mn}[/tex]
c) [tex](2\times3)^{10}=6^{10}[/tex] fairly self-explanatory because [tex]2\times3=6[/tex]
d) [tex]2^{10}\times3^{10}=6^{10}[/tex] because [tex]a^m\times b^m=ab^m[/tex]
Hence a is the answer.
2) [tex]25\frac12\div\frac12=\frac{51}2\times\frac21=51[/tex]
Hence b is the answer
Nutritional information for macraroni and broccoli is given in a table. How many servings of each would it take to get exactly 22 grams of protein and 64 grams of of carbohydrates
Using a system of equations, it is found that it would take 2 servings of macaroni and 8 servings of broccoli to get the desired amount.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable M: Servings of macaroni.Variable B: Servings of broccoli.Researching the problem on the internet, each serving of macaroni has 3 grams of protein, while each serving of broccoli has 2 grams. Since 22 grams of protein are needed, we have that:
3M + 2B = 22.
Each serving of macaroni has 16 grams of carbohydrates, while each serving of broccoli has 4 grams. Since 64 grams of carbohydrates are needed, we have that:
16M + 4B = 64
Simplifying by 4:
4M + B = 16 -> B = 16 - 4M
Replacing in the first equation:
3M + 2B = 22
3M + 2(16 - 4M) = 22
5M = 10
M = 10/5
M = 2.
B = 16 - 4M = 16 - 8 = 8
2 servings of macaroni and 8 servings of broccoli are needed.
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Consider function f. f(x) = cube root of x - 7. Select g(x) so that f(g(x)) = g(f(x)) = x for all values of x.
The function g(x) is [tex]g(x) = (x + 7)^3[/tex]
How to determine the function g(x)?The function f(x) is given as:
[tex]f(x) = \sqrt[3]{x} - 7[/tex]
If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.
So, we have:
[tex]f(x) = \sqrt[3]{x} - 7[/tex]
Rewrite as:
[tex]y = \sqrt[3]{x} - 7[/tex]
Swap x and y
[tex]x = \sqrt[3]{y} - 7[/tex]
Add 7 to both sides
[tex]x + 7 = \sqrt[3]{y}[/tex]
Take the cube of both sides
[tex]y = (x + 7)^3[/tex]
This implies that
[tex]g(x) = (x + 7)^3[/tex]
Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]
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NEED HELP ASAP PLEASE
20 POINTS !!!
The most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equations:
0.02x - 0.05y = -0.38
0.03x + 0.04y = 1.04
We can write above equations as follows:
2x - 5y = -38
3x + 4y = 104
After solving with the substitution method:
x = 16
y = 14
-20 ≤ x ≤ 20
-15 ≤ x ≤ 15
Thus, the most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.
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which graph represents the function h(x)=IxI+0.5
Answer:
It should look like a v with the origin at +0.5
Step-by-step explanation:
Factorize x^2+√4x+2x+2
[tex]factorize \: {x}^{2} + \sqrt{4x} + 2x + 2 [/tex]
Answer:
x^2+4x+2
Step-by-step explanation:
√4 = 2
=x^2+2x+2x+2
add the ones that are the same (2x+2x)
x^2+4x+2
Becky owns a business in an area that has an assessment rate of . The property tax rate is per . What is the effective tax rate?
The effective tax rate based on the assumed information is 2.5%.
How to illustrate the tax?Let's assume that the figures are:
Income tax expense = $50
Income before tax = $2000
It should be noted that tax rate is calculated as:
= Income tax expense / Income before tax
= 50/2000
= 0.025
= 2.5%
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A number generator was used to simulate the percentage of people in a town who join a health club yearly. The process simulates randomly selecting 100 people from the town and was repeated 20 times. The percentage of people who join a health club yearly is shown in the dot plot. Which statement is most likely true about the population of the town? Most likely, 50% of the people in the town join a health club yearly. Most likely, about 40% to 60% of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100 A number generator was used to simulate the percentage of people in a town who join a health club yearly . The process simulates randomly selecting 100 people from the town and was repeated 20 times . The percentage of people who join a health club yearly is shown in the dot plot . Which statement is most likely true about the population of the town ? Most likely , 50 % of the people in the town join a health club yearly . Most likely , about 40 % to 60 % of the people in the town 0 10 20 acer 30 40 50 60 70 80 : 90 100
The statement that's is likey true about the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.
How to illustrate the information?It should be noted that a dot plot simply gives a pictorial representation of the information given.
In this case, the population of the town is that most likely about 40% to 60% of the people Jon the health club yearly.
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Answer: Most likely, about 40% to 60 % of the people in the town join a health club yearly.
Step-by-step explanation:
Which represents the solution set of the inequality 5x-921?
O 0 xs 1/2/2
O x21/12/2
O x26
O x≤6
The solution of the given Inequality is; D: x ≤ 6
How to find the solution of an Inequality?We want to find the solution to the Inequality;
5x - 9 ≤ 21
Using Addition property of equality, add 9 to both sides to get;
5x ≤ 30
Using division property of equality, divide both sides by 5 to get;
x ≤ 6
All real numbers less than or equal to 6
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I need the correct answer for questions 1
The truth values of the propositions are false, true and false
How to determine the true values?The Boolean variables are given as:
p = false
r = false
q = true
s = true
The truth values of the propositions are as follows:
1. (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s)
As a general rule:
∧ means and
¬ not
∨ or
So, we have:
(true → (false ∧ ¬ false)) ∧ ((false → (false ∨ true)) ∧ true)
¬ false= true.
So, we have:
(true → (false ∧ true)) ∧ ((false → (false ∨ true)) ∧ true)
false ∧ true = false and false ∨ true = true
So, we have:
(true → false) ∧ ((false → true) ∧ true)
false → true = true and true → false = false
So, we have:
(false) ∧ (true ∧ true)
true ∧ true = true
So, we have:
false ∧ true
Lastly
false ∧ true = false
Hence, the truth value of (s → (p ∧ ¬ r)) ∧ ((p → (r ∨ q)) ∧ s) is false
2. ((p ∧ ¬ q) → (q ∧ r)) → (s ∨ ¬q)
This means
((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true)
Using the established rules in (1), we have:
((false ∧ false) → (true ∧ false)) → (true ∨ false)
This gives
((false → false)) → true
This gives
true → true
Lastly, we have:
true
Hence, the truth value of ((false ∧ ¬ true) → (true ∧ false)) → (true ∨ ¬true) is true
3. (p → q) ∧ (q → r)
This gives
(false → true) ∧ (true → false)
Using the established rules in (1), we have:
true ∧ false
This gives
false
Hence, the truth value of (p → q) ∧ (q → r) is false
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah
The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.
What is the distance about?Note that At the point H, there is found to be an intersection between the distance taken by both people involve so:
Y (a)= 10 + 2x ------ Josiah
Y (0) = 3x ----- Chana
If Y (a)= Y (0)
Then:
10 + 2x = 3x
x = 10
F = x = 20
Y (o) = 60
If x = 20
= then Y(0) = 3 x 20
= 60
Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.
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Find LP if C= 16 please help me ASAP PLEASE AND THANK YOU
Answer:
8 * sqrt2
Step-by-step explanation:
the area of a square can be found by squaring the length of the diagonal and then dividing it by 2. 16^2 / 2 = 128. if the area of a square is 128, each side is sqrt 128 = 8 * sqrt2
The center of a sphere is
a line segment from the center point to the surface of the sphere.
a fixed point equidistant from all points on the surface of the sphere.
a three-dimensional circle in which all points are equidistant from a fixed point.
the same as the base of the sphere.
Answer:
Center of the Sphere is a fixed point in its interior which is equidistant from each point on sphere. Option A is not right because it says center is line segment. Option B is right as it says it is fixed and equidistant from point of surface.
Step-by-step explanation:
Desperately need answer to this question
Answer:
20x^2 + 47x + 24
Step-by-step explanation:
The area of a rectangle is LENGTH * WIDTH. From the diagram, we see that LENGTH = 4x + 3 and WIDTH = 8 + 5x. Therefore the area is:
A = LENGTH*WIDTH
= (4x+3)(5x+8)
= 20x^2 + 32x + 15x + 24
= 20x^2 + 47x + 24
Answer: C. 20x²+47x+24
Step-by-step explanation: Use the FOIL Method (First, Outer, Inner, Last). Equation: (5x+8) (4x+3). Hope this helps!
the average monthly salary of m male emploees and f female employees of a company is $2000. if the average monthly salary of the male emploees is $(b+200)find the average monthly salary of the the female employees
The average monthly salary of the female employees is $900.
What is an Equation ?An equation is a mathematical statement that equates algebraic expression to other algebraic expressions or constants by an equal sign that helps to determine the value of unknown variables.
It is given that
the average of the monthly salary of female and male employees is $ 2000
Let the average monthly salary of the female employees is $b
It is again given that
The average monthly salary of the male employees is $(b +200)
so , the equation can be formed as
b + b + 200 = 2000
2b + 200 = 2000
2b = 2000 - 200
2b = 1800
b = $900
The average monthly salary of the female employees is $900.
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10) Choose the solution for each linear system.
(3,0)
(-3,-1)
(2,-1)
(-2,1)
(x-2y=4
4x + 2y = 6
11) Choose the solution for each linear system.
(2,4)
O(-2,-4)
O (4,2)
O(-4,-2)
[6x-2y = -4
-4x+3y=-4
Answer:
10. C. (2, -1)11. B. (-2, -4)Step-by-step explanation:
10.
[tex]\left \{ {{x-2y=4} \atop {4x+2y+6}} \right.[/tex]
The y values cancel out if you add the equations
5x = 10
x = 2
plug in x
2 - 2y = 4
-2y = 2
y=-1
Answer: C. (2, -1)
11.
[tex]\left \{ {{6x-2y=-4} \atop {-4x+3y=-4}} \right.[/tex]
In order to get terms to cancel out, multiply the top by 3 and bottom by 2
[tex]\left \{ {{18x-6y=-12} \atop {-8x+6y=-8}} \right.[/tex]
The y values cancel out if you add the equations
10x = -20
x = -2
plug in x
6(-2) - 2y = -4
-12 - 2y = -4
-2y = 8
y = -4
Answer: B. (-2, -4)
Given: PB tangent PV, PU secants
If m VU = 80° and m ST = 40°, then m <2 =
A. 60
B. 40
C. 20
The measure of <2 is 60.
what is tangent?The tangent is defined as a line touching circles or an ellipse at only one point.
given:
VU = 80° and ST = 40°
By using theorem,
The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.
<2= 1/2 (80+ 40)
<2= 60
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System AAA \text{\quad}start text, end text System BBB
\begin{cases}-3x+12y=15\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−3x+12y=15
7x−10y=−2
\begin{cases}-x+4y=5\\\\7x-10y=-2\end{cases}
⎩
⎪
⎪
⎨
⎪
⎪
⎧
−x+4y=5
7x−10y=−2
1) How can we get System BBB from System AAA?
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
For systems A and B we have:
1) Change the first equation in A by a multiple of itself. (the multiple is 1/3).
2) Yes, the systems are equivalent.
How to get system B from system A?
Here we have the systems of equations:
A:
-3x + 12y = 15
7x - 10y = -2
B:
-x + 4y = 5
7x - 10y = -2
Notice that the second equation is the same in both systems, so we only need to work with the first ones.
If we take the first equation in system A:
-3x + 12y = 15
If we divide both sides by 3, we get:
-x + 4y = 5
Which is the first equation of B.
So we just need to replace the first equation in system A by a multiple of itself to get system B.
Because of that, we conclude that both systems are equivalent (because are made of the same equations) which means that both systems have the same solutions.
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Answer: C), Yes
Step-by-step explanation:
What is slope of the line?
y+6=13(x−4)
−13
1 3
4
6
Answer:
Therefore the slope is 13
Step-by-step explanation:
Using Slope intercept formula y = mx + b.
Note : m is the slope ( the number near x).
y+6=13(x−4)
y+6 = 13x - 52
Add -6 to both sides
y+ 6- 6 = 13x- 52- 6
y= 13x -58
Therefore the slope is 13
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line y+6=13(x-4)
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
The slope of this particular graph is: the constant multiplied by the parentheses.
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope \:13}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Please help me with this math problem
Answer:
the MEAN for class a is 72.6
the MEAN for class b is 84.0
if you take these means and compare them, you can see that on average, class B performed better.
the MEDIAN for class a is 72
the MEDIAN for class b is 85
Step-by-step explanation:
Another geometry question thanks!
For the given right triangle, we have:
L = 57°ML = 4.5NL = 7.5How to get the dimensions of the given triangle?Here we have a right triangle, remember that the sum of the internal angles of a triangle must be 180°, then:
N + M + L = 180°
We can see that:
N = 37°
M = 90°
Then:
L = 180° - N - M = 180° - 37° - 90° = 53°
Also, if we step on N, the adjacent cathetus measures 6 units, then we can use the relations:
tan(37°) = (opposite cathetus)/(adjacent cathetus)
tan(37°) = ML/6
tan(37°)*6 = ML = 4.5
cos(37°) = (adjacent cathetus)/(hypotenuse)
cos(37°) = 6/NL
NL = 6/cos(37°) = 7.5
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