Answer:
Step-by-step explanation:ik
Final answer:
To find the variance, calculate the average of the squared differences between each data point and the mean. The standard deviation is found by taking the square root of the variance.
Explanation:
To calculate the variance, follow these steps:
Find the mean of the data set.
For each data point, subtract the mean and square the result.
Find the average of the squared differences.
To calculate the standard deviation, take the square root of the variance.
For example, if the data set is {2, 4, 6, 8, 10}, the mean is 6. The squared differences are {(2-6)^2, (4-6)^2, (6-6)^2, (8-6)^2, (10-6)^2}, which equals {16, 4, 0, 4, 16}. The average of the squared differences is (16+4+0+4+16)/5 = 40/5 = 8. Therefore the variance is 8. The standard deviation is the square root of the variance, so in this case, the standard deviation is √8 = 2.83.
a projectile is thrown upward so that it's distance above the ground after T seconds is H equals -16t^2 + 672 T. After how many seconds does it reach its maximum height?
Step-by-step explanation:
T = time in seconds
H = distance
Tground = time to return to ground
Tmax = time at maximum height
H = -16T^2 + 672T...eqn 1
projectile returns to ground at H =0,
subs for H in eqn 1...
0 = -16T^2 + 672T
solving for T we get...
16T^2 = 672T
=> Tground = 42secs
Tmax = 0.5 Tground = 21secs
Express -5 2/5 as an improper fraction. help asap!!!!
Answer:
[tex]\large\boxed{-5\dfrac{2}{5}=-\dfrac{27}{5}}[/tex]
Step-by-step explanation:
[tex]\bold{Method\ 1}:\\\\5=\dfrac{5\cdot5}{5}=\dfrac{25}{5}\\\\-5\dfrac{2}{5}=-\left(5+\dfrac{2}{5}\right)=-\left(\dfrac{25}{5}+\dfrac{2}{5}\right)=-\dfrac{25+2}{5}=-\dfrac{27}{5}\\\\\bold{Method\ 2:}\\\\\text{Multiply the integer by the denominator and add it to the numerator.}\\\\-5\dfrac{2}{5}=-\dfrac{(5)(5)+2}{5}=-\dfrac{25+2}{5}=-\dfrac{27}{5}[/tex]
Answer:
5 x 5 + 2
= -27/5 (5 is denominator)
Find the GCF of 12x^2y and 27xy^3z
Step-by-step explanation:
all work is shown and pictured
The GCF of 12x^2y and 27xy^3z is 3xy.
What is GCF?The full sort of GCF is greatest divisor. it's also referred to as highest common factor.
How to find GCF?we have to seek out GCF of
We can write them as:
1)2*2*3*x*x*y
2)3*3*3*x*y*y*y*z
GCF=3*x*y
=3xy
Hence the best common measure of 12x^2y and 27xy^3z is 3xy.
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A woman who is 6-ft tall casts a 4.5-foot shadow at the same time that a building casts a 75-foot shadow. What is the height of the building in feet?
Answer:
The height of the building is [tex]100\ ft[/tex]
Step-by-step explanation:
Let
h ----> the height of the building in feet
we know that
Using proportion
[tex]\frac{6}{4.5}=\frac{h}{75}\\ \\h=6*78/4.5\\ \\h=100\ ft[/tex]
I took the test and got 100 ft correct
I need help with this
Answer:
-1,1,3
Step-by-step explanation:
The zeros,roots and the x-intercept are the same, so see where the graph touches the x axis and that or thosepoints is/are the zeros
What is the slope of the line represented by the equation y = –2/3 – 5x?
Answer:
The slope is m=-5
Step-by-step explanation:
we know that
The equation of the line into slope intercept form is equal to
y=mx+b
where
m is the slope
b is the y-intercept
In this problem we have
y=-(2/3)-5x
so
the slope is equal to
m=-5
the y-intercept is equal to
b=-2/3
Miles paid $5824, including 4% sales tax, for an out-of-state purchase of a car. In order to calculate the amount of sales tax he owes in his state, he must first determine the price of the car without sales tax. How much did the car cost before sales tax? This one is a little bit tricky. The amount you need to find the sales tax of is not know. Let the original price be x. Then, 4% of that price is 0.04x. Adding the original price and the sales tax, we get the amount paid. Therefore, the equation is
X + 0.04x = 5824
Answer:
$5600
Step-by-step explanation:
Original Cost = x
Total Cost = $5824
Sales Tax = 4% or 0.04
Problem Setup
(Original Cost) + 4% (Original Cost) = Total Cost
x + 0.04x = 5824
1x+ 0.04x = 5824
1.04x = 5824
1.04x/1.04 = 5824/1.04
x=5600 Original Cost
To Check math multiply 5600 x 0.04 = 224.
Then add $5600 + $224 = $5824
The price of the car before sales tax is $5600.
To determine the cost of the car before sales tax, we can use the equation provided:
[tex]x + 0.04x = 5824[/tex]
Here, [tex]x[/tex] represents the original price of the car before sales tax, and [tex]0.04x[/tex] represents the amount of sales tax, which is 4% of the car's price.
First, combine the terms on the left side of the equation:
[tex]1x + 0.04x = 1.04x[/tex]
Therefore, the equation simplifies to:
[tex]1.04x = 5824[/tex]
Next, to solve for [tex]x[/tex], divide both sides of the equation by 1.04:
[tex]x = \frac{5824}{1.04}[/tex]
Calculating the right side:
[tex]x = 5600[/tex]
Select all that apply. Which postulates are discussed in this lesson?
Try to put in 9 and 10
given f(x)=2x^2-8x+6 and g(x)=3x-1 find f(x) +g(x)
a. 2x^2+5x+5
b.2x^2-11x+7
c. 2x^2-5x+5
d.2x^2-5x-5
For this case we have the following functions:
[tex]f (x) = 2x ^ 2-8x + 6\\g (x) = 3x-1[/tex]
We must find f (x) + g (x):
We have to:
[tex]f (x) + g (x) = 2x ^ 2-8x + 6 + (3x-1)\\f (x) + g (x) = 2x ^ 2-8x + 6 + 3x-1[/tex]
We add similar terms:
[tex]f (x) + g (x) = 2x ^ 2-5x + 5[/tex]
Answer:
[tex]f (x) + g (x) = 2x ^ 2-5x + 5[/tex]
OPTION C
What is another name for a cord that passes through the center of a circle
Answer:
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter, and is the longest chord.
Step-by-step explanation:
Answer:
Diameter
Step-by-step explanation:
Solve for u -5/2u = 15
Answer:
U = -1/6
How to solve:
Multiply both sides by 2U to get rid of the denominator and you should end up with
[tex] - 5 = 15(2u)[/tex]
then multiply and devide to get your U by itself.
you should then get
[tex]u = - \frac{1}{6} [/tex]
after symplifying.
Answer:
Answer:
u=−10
Step-by-step explanation:
Let's solve your equation step-by-step.
u− 5 /2 u=15
Step 1: Simplify both sides of the equation.
u− 5/ 2 u=15
u+ −5 /2 u=15 (u+ −5 2 u)=15
(u+ −5 2 u)=15(Combine Like Terms)
−3 /2 u=15
−3 /2 u=15
Step 2: Multiply both sides by 2/(-3).
( 2 −3 )*( −3 2 u)=( −3 )*(15)
u=−10
A professor has eight different tasks to assign, one to each of her eight teaching assistants. In how
many different ways could she make the assignments?
Answer:
40320
Step-by-step explanation:
There are 8 different people we could assign to the first task. Now there are 7 tasks and 7 people left. There are 7 different people we could assign to the next task. And so on
8 *7*6*5*4*3*2*1
8!
40320
Final answer:
The professor can assign eight different tasks to her eight teaching assistants in 40,320 different ways, calculated by the factorial of eight (8!).
Explanation:
The question pertains to the number of ways to assign eight different tasks to eight teaching assistants. This problem can be solved using the concept of permutations, which is a fundamental principle in combinatorics, a branch of mathematics.
To find the number of different permutations of eight distinct items (the tasks), we would calculate 8!, which signifies factorial of eight. This represents the product of all positive integers up to 8:
8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320Therefore, there are 40,320 different ways the professor can make the assignments to her eight teaching assistants.
the roots of the equation x^2-6x+7=0 are a and b.
find a quadratic equation with roots a+1/b and b + 1/a.
please reply ASAP as i have an exam tomorrow!!
Answer:
[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]
Step-by-step explanation:
step 1
Find the roots of the quadratic equation
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} -6x+7=0[/tex]
so
[tex]a=1\\b=-6\\c=7[/tex]
substitute in the formula
[tex]x=\frac{6(+/-)\sqrt{-6^{2}-4(1)(7)}} {2(1)}[/tex]
[tex]x=\frac{6(+/-)2\sqrt{2}} {2}[/tex]
[tex]x=3(+/-)\sqrt{2}[/tex]
[tex]x1=3(+)\sqrt{2}[/tex]
[tex]x2=3(-)\sqrt{2}[/tex]
The roots of the equation are a and b
so
[tex]a=3(+)\sqrt{2}[/tex]
[tex]b=3(-)\sqrt{2}[/tex]
step 2
Find a quadratic equation with roots a+1/b and b + 1/a
so
[tex]a+\frac{1}{b} =(3+\sqrt{2})+\frac{1}{3-\sqrt{2}} =\frac{9-2+1}{3-\sqrt{2}} =\frac{8}{3-\sqrt{2}}=\frac{8}{3-\sqrt{2}}*(\frac{3+\sqrt{2}}{3+\sqrt{2}})=\frac{8}{7}(3+\sqrt{2})[/tex]
[tex]b+\frac{1}{a} =(3-\sqrt{2})+\frac{1}{3+\sqrt{2}} =\frac{9-2+1}{3+\sqrt{2}} =\frac{8}{3+\sqrt{2}}=\frac{8}{3+\sqrt{2}}*(\frac{3-\sqrt{2}}{3-\sqrt{2}})=\frac{8}{7}(3-\sqrt{2})[/tex]
The quadratic equation is equal to
[tex]y=(x-\frac{8}{7}(3+\sqrt{2}))(x-\frac{8}{7}(3-\sqrt{2}))[/tex]
[tex]y=x^{2} -\frac{8}{7}(3-\sqrt{2})x-\frac{8}{7}(3+\sqrt{2})x+\frac{64}{49}(7)[/tex]
[tex]y=x^{2} -\frac{48}{7}x+\frac{64}{7}[/tex]
i want the answer................
Answer:
AB = CD = 3√5
Step-by-step explanation:
We use Pythagoras' Theorem.
AB² = CD² = 3²+6² = 9+36 = 9·(1+4) = 9·5
=> AB = CD = √(9·5) => AB = CD = 3√5
Which best describes the meaning of the term theorem?
Answer: Ok, this have come up with. Here are 4 different definitions theorem could possiably mean :)
Mathematics. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas.a rule or law, especially one expressed by an equation or formulaLogic. a proposition that can be deduced from the premises or assumptions of a system.an idea, belief, method, or statement generally accepted as true or worthwhile without proof.
Hope that helps you out :D
Answer this question thanks
First divide 5 to both sides to isolate p. Since 5 is being multiplied by p, division (the opposite of multiplication) will cancel 5 out (in this case it will make 5 one) from the right side and bring it over to the left side.
20 ≥ 5p
20 ÷ 5 ≥ 5p ÷ 5
4 ≥ 1p
4 ≥ p
For the graph will you have a empty or colored in circle?
If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.
If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.
Which direction will the ray go?
If the variable is LESS then the number then the arrow will go to the left of the circle.
If the variable is MORE then the number then the arrow will go to the right of the circle.
In this case your inequality is:
4 ≥ p OR p ≤ 4
aka 4 is greater then p OR p is less then 4
This means that the graph will have an colored circle and the arrow will go to the left of 4. Look at image below.
Hope this helped!
~Just a girl in love with Shawn Mendes
Which expression is equal to...
1: (4^5)(4^-2)/4^-7
2: 4^-4
3: 4^0
4: 4^5/4^-9
Jane bought a new rectangular placemat with an area of 126 square inches. The length of the placemat is four times the quantity of nine less than half its width.
Complete the equation that models the area of the placemat, in terms of the width of the placemat, w.
= w2 - w
The width of the placemat is inche
Answer:
126 = 2w² -36w21 inchesStep-by-step explanation:
The length is described as 4(-9 +w/2), which simplifies to 2w-36. The area is the product of length and width, so is ...
Area = width×length
126 = w(2w -36) = 2w² -36w
__
This equation can be divided by 2, then the square completed to give ...
w² -18w = 63
w² -18w +81 = 144 . . . . add 81 to complete the square
(w -9)² = 12² . . . . . . . . . show as squares
w -9 = 12 . . . . . . . . . . . . take the positive square root
w = 12 +9 = 21
The width of the placemat is 21 inches.
Answer:
[tex]126in^2=2w^2-36w[/tex] and w= 21 inches.
Step-by-step explanation:
The placemat has an area of [tex]126in^2[/tex]. Now, let's call w to the width, the exercise says that the length of the placemat is four times the quantity of nine less than half its width, that is
length = 4(w/2-9).
Now, the area is length*width, so
[tex]A=w*4(\frac{w}{2}-9)= \frac{4w^2}{2}-36w = 2w^2-36w.[/tex]
and we know that [tex]A=126in^2[/tex], so
[tex]126in^2=2w^2-36w.[/tex]
Now, let's find the solution.
[tex]2w^2-36w-126=0[/tex] is a quadratic formula of the form [tex]ax^2+bx+c[/tex] with a=2, b= -36 and c = -126. The solutions will be
[tex]w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]w=\frac{-(-36)\pm\sqrt{36^2-4(2)(-126)}}{2a}[/tex]
[tex]w=\frac{36\pm\sqrt{1296+1008}}{2*2}[/tex]
[tex]w=\frac{36\pm\sqrt{2304}}{4}[/tex]
[tex]w=\frac{36\pm48}{4}[/tex]
[tex]w=\frac{36+48}{4}[/tex] or [tex]w=\frac{36-48}{4}[/tex]
[tex]w=\frac{84}{4}[/tex] or [tex]w=\frac{-12}{4}[/tex]
as we are searching a distnace, we are going to use the positive solution, that is
[tex]w=\frac{84}{4}= 21.[/tex]
Then, the width is 21 inches.
A diver descends at a rate of 12 feet per minute at this rate where will the diver be in relation of surface after 4 minutes
Answer:
48 feet
Step-by-step explanation:
Distance = rate × time
d = 12 ft/min × 4 min
d = 48 ft
The diver will be 48 feet below the surface.
Answer:
-48 ft
Step-by-step explanation:
The unit rate of descent is
-12 ft
-----------
1 min
and so after 4 minutes, the diver will be 48 ft beneath the surface:
-12 ft
----------- * 4 min = -48 ft
1 min
Which expression is equivalent to (2x^2)(3x^3)(4x)^2?
(2x^2)(3x^3)(4x)^2
=6x^5(16x^2)
=96X^7
Answer:
24 x^7
Step-by-step explanation:
(2 x^2)(3 x^3)(4 x)^2 = 2*3*4 * x² * x³ * x² = 24 x^7
Which equation represents f(x)?
Answer:
C. [tex]y=\sqrt[3]{-x} -1[/tex]
Step-by-step explanation:
Consider the eparent function [tex]y=\sqrt[3]{x}[/tex] The graph of this function is shown in the attached diagram - red curve.
Reflect this graph across the y-axis, you'll get the blue line which equation is
[tex]y=\sqrt[3]{-x}[/tex]
Translate this graph 1 unit down, then you'll get green line (that is exactly the graph from your image) and the function for this line is
[tex]y=\sqrt[3]{-x} -1[/tex]
Which statement best describes the function below?
f(x) = 2x^3 + 2x^2-x
) A. It is a many-to-one function.
B. It is a one-to-one function.
C. It is not a function.
D. It fails the vertical line test.
A. It is a many-to-one function.
Step-by-step explanation:Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:
[tex]f(x) = 2x^3 + 2x^2-x[/tex]
When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:
A. It is a many-to-one function.True
A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line [tex]y=0.5[/tex], and you can see from the first figure below that [tex]y=0.5[/tex] is mapped onto [tex]x=-1.241 \ x=-0.344 \ and \ x=0.585[/tex]. so this is a many-to-one function.
B. It is a one-to-one function.FalseSince this is a many-to-one function, it can't be a one-to-one function.
C. It is not a function.False
Indeed, this is a function
D. It fails the vertical line test.False
It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.
The following table shows the number of comments on each of Omar's 9 most recent spcial media posts.
Based on this data, what is reasonable estimate of the probability that Omar's next post will get no comments?
CHOOSE 1 ANSWER:
A.) 0/27
B.) 4/9
C.) 4/5
D.) 27/27
The probability that the next post will have 0 comments is P = 4/9.
How to get the probability?
The probability will be equal to the quotient between the number of posts with no comments and the total number of posts.
We know that there are 9 posts, and by looking at the table, we can see that 4 out of these 9 posts have 0 coments.
Then the probability that the next post will have 0 comments is:
P = 4/9
So the correct option is B.
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Angles HJG and GIH contain the same endpoints at arc GH. Angle HJG measures 35 degrees. What is the angle measure of GIH?
The angle measure of GIH is 35 degrees. The corresponding angles theorem guarantees that when two angles are formed by intersecting lines and share the same endpoints at an arc, they will have equal measures.
Since angles HJG and GIH contain the same endpoints at arc GH, they are corresponding angles formed by intersecting lines with a transversal. According to the corresponding angles theorem, when two lines are intersected by a transversal, the corresponding angles are congruent.
Given that angle HJG measures 35 degrees, we can conclude that angle GIH also measures 35 degrees. This is because they are corresponding angles and share the same endpoints at arc GH.
Therefore, the angle measure of GIH is 35 degrees. The corresponding angles theorem guarantees that when two angles are formed by intersecting lines and share the same endpoints at an arc, they will have equal measures. In this case, both angles HJG and GIH have an angle measure of 35 degrees.
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Which equation is represented by the graph below?
Answer:
That's [tex] y = \ln x[/tex]
Step-by-step explanation:
[tex]f(1) = \ln 1 = 0[/tex]
[tex]f(e) = \ln e = 1[/tex]
[tex]f(1/e) = \ln (1/e) = -1[/tex]
Seems right.
What is the benefit of converting measures in a ratio to the same unit
Answer:
so you can simplify the ratio
Step-by-step explanation:
How do you solve the equation y=2x^2+6x-80 for solution sets?
The solution set for the quadratic expression given is : (-8, 5)
Using the expression given :
y = 2x² + 6x - 80divide through by 2
y = x² + 3x - 40
As a quadratic expression ;
x² + 3x - 40 = 0
factors whose product gives -40 and addition gives 3
x² + 8x - 5x - 40
factorize
x(x + 8) -5(x + 8)
(x + 8) = 0 or (x - 5) = 0
x = -8 or x = 5
Hence, the solution set is (-8 or 5)
int(1 \(1 + {e}^{x} )
Answer:
[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx}= x - \ln(1 + e^{x}) + C\end{aligned}[/tex].
Step-by-step explanation:
The first derivative of the denominator [tex]1 + e^{x}[/tex] is [tex]e^{x}[/tex]. Rewrite the fraction to obtain that expression on the numerator.
[tex]\begin{aligned}\frac{1}{1 + e^{x}} &= \frac{1 + e^{x}}{1 + e^{x}} - \frac{e^{x}}{1+e^{x}}\\&=1-\frac{e^{x}}{1+e^{x}}\end{aligned}[/tex].
In other words,
[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\end{aligned}[/tex].
Apply [tex]u[/tex]-substitution on the integral [tex]\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx}[/tex]:
Let [tex]u = 1 + e^{x}[/tex]. [tex]u > 1[/tex].
[tex]du = e^{x}\cdot dx[/tex].
[tex]\displaystyle \int{\frac{e^{x}}{1+e^{x}}\cdot dx} = \int{\frac{du}{u}} = \ln{|u|} = \ln{u} +C = \ln{(1+e^{x})}+C[/tex].
Therefore
[tex]\begin{aligned}\int{\frac{1}{1 + e^{x}}\cdot dx} &= \int{dx} - \int{\frac{e^{x}}{1+e^{x}}\cdot dx}\\ & = x - \ln{(1 + e^{x})}+C\end{aligned}[/tex].
| IF THE TEMPERATURE WAS -41°F AND THEN
WARMED 52°F. WHAT IS THE TEMPERATURE?
3
Hey there! :)
If the temperature was at -41 F then warmed by 52 F, then what is our current temperature?
Simply do -41+52. Another way that your mind can do this is by rearranging this to look like this : 52 - 41
Because we are already very accustomed to doing this, we know that 52-41 is equal to 11. Therefore, -41+52 is very simply 11.
This means that our current temperature is 11 degrees Fahrenheit.
Hope this helped! :)
which of the following is a conditional probability?
A.the probability that a person will be born with blue eyes or struck by lightning
B.the probability that a person will buy a red car.
C.the probability that a person will order dessert given that they ordered a steak for dinner.
D.the probability that a person will not purchase a cell phone.
The probability that a person will order dessert given that they ordered a steak for dinner, this is an example of conditional probability.
What is conditional probability?Given that another event (B) has previously occurred, the likelihood of an event (A) occurring.
Event A in Option(C) - A person will order dessert
Event B in Option(C) - A person will order steak for dinner
Event A will only occur if the event B has already completed, hence according to the definition this is an example of conditional probability.
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