Step-by-step explanation:
Multiply the factors
[tex](x - 1)(x + 1)(x + 3)[/tex]
[tex]( {x}^{2} - 1)(x + 3)[/tex]
[tex]{x}^{3} + 3 {x}^{2} - x - 3[/tex]
The highest exponent is 3, so the degree is 3
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]
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:
Simplify
9/2 - 3√7 +8 - 28
0.11√2-5√7
11√4-5√14
6 5
6 9
Step-by-step explanation:
gfyiaycoeayclpb tydivh.
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 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:
Solve algebraically
X+4=-2
Answer:
x=-6
Step-by-step explanation:
-6+4=-2
Give brainliest please
Find the greatest common factor of the
following monomials:
9w³
21w
15w6
Enter the correct answer.
Answer:
Step-by-step explanation:
9w^{321+15+6}
9w^{342}
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 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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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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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 60 degrees at midnight and the high and low temperature during the day are 73 and 47 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
D(t)=
Answer:
D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)
Step-by-step explanation:
The temperature at any time t can be represented as:
D(t)=A+B*sin(2*pi*t/T)+C*cos(2*pi*t/T)
where A is the average temperature, B is the amplitude of the sine wave, C is the amplitude of the cosine wave, and T is the period.
In this case, we are given that the average temperature is 60, the high temperature is 73, and the low temperature is 47. We can therefore calculate that the amplitude of the sine wave is 23 and the amplitude of the cosine wave is 26. The period is 24 hours. Therefore, the equation for the temperature in terms of time is:
D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)
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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The scatter plot shows the relationship between the amount of rain received in a year and the average diameter of a fruit in a particular orchad that year
The regression equation is mathematically given as
[tex]\=Y = 5 + 0.3 X[/tex]
This is further explained below.
What is the Regression equation?The line is passing through (0, 5) and (15, 10).
Generally, the equation for Slope is mathematically given as
[tex]S=\frac{ (10 - 5)}{(15 - 0) }[/tex]
Therefore
S= 5/15
S= 1/3
S= 0.3
Intercept = 5
In conclusion,Regression equation:
[tex]\=Y = 5 + 0.3 X[/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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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)
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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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
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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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:
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
1/6z= -10
A. -60
B. -4
C. -5/3
D. -16
Answer:
z = -60
Step-by-step explanation:
1/6z= -10
To find the value for z, multiply each side by 6
6*1/6z= -10*6
z = -60
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!
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:
Which of the following numbers is shown plotted on the number line?
Answer:
-2 3/8
Step-by-step explanation:
since point A is left of 0, it means it is a negative value.
so, the positive answer options are automatically out.
then we see that point A is 2 full units and a little bit left of 0.
that means it has to be lower than -2 but higher than -3.
-22/7 = -3 1/7
so, that is too low.
-3 7/8 is too low.
so, that leaves -2 3/8 (confirmed also by the fact that A is a little bit higher than half between -2 and -3, which is the case for -2 3/8).
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
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]
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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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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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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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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