Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{55}{10} = 5.5[/tex]
You want to prove that FHG is similar to RXS by the SSS Similarity Theorem. Complete the proportion that is needed to use this theorem.
Answer:
[tex]\frac{FH}{RX} =\frac{HG}{XS} =\frac{FG}{RS}[/tex]
Step-by-step explanation:
The order of the letters matters in any similarity theorem.
When triangle FHG is similar to triangle RXS, the lengths of FH must be similar to RX.
When 2 similar lines are divided, that number is the factor by which one triangle can be dilated to match the other.
That being said, each of these proportion statements can be read as individual division expressions that equal the next division expression.
This means [tex]FH\div RX = HG\div XS = FG\div RS[/tex].
If you look at it this way, you can see that the sides you need to fill in must be the corresponding similar sides, so that you end up with the factor for the dilation of the 2 triangles.
HELP ASAP AND GET 20 POINTS!!!
Answer:
A
Step-by-step explanation:
point H is the point of intersection of the perpendicular bisectors of the triangle's sides and is the circumcentre.
Answer:
A. Circumcenter
Step-by-step explanation:
this is the point that has the same distance from all 3 vertexes.
being on the median line of DE, every point of that line has the same distance to D and E.
being also on the median line of FE means it has the same distance from F and E as every other point on that line.
and the same for DF.
H as the crossing point of all 3 median lines is the only point that has the same distance to D, E and F.
so, H is the center of a circle that goes through all 3 points.
. A special safe lets you choose from 9 symbols for a 3-symbol-long pass code. You may enter a symbol any number of times. How many potential pass codes are there
The question is an illustration of combination and there are 729 potential pass codes available
How to determine the number of potential pass codes?The given parameters are
Symbols available = 9
Length of pass code = 3
From the question, we understand that a symbol may be entered any number of times.
This means that each of the 9 available symbols can be used three times
So, the number of potential pass codes is
Passcodes = 9 * 9 * 9
Evaluate the product
Passcodes = 729
Hence, there are 729 potential pass codes available
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In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as:
In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.
Leitmotiv, from the German "leading motive," is a recurrent musical motif that typically appears in operas but can also be found in symphonic poems.Overture to a concert. Romantic-era concert piece for orchestra in one movement, frequently based on a literary program.What is serious opera called?
Opera seria, or "serious opera," is an Italian operatic genre that was popular in 18th-century Europe. The genre is commonly referred to as Neapolitan opera since it first appeared in the late 17th century, particularly in the works of Alessandro Scarlatti and other composers based in Naples.What is Wagnerian leitmotif?
A theme of easily recognizable melodic, rhythmic, or harmonic identity, first used in connection with a certain character of incident, and which returns time and time again, always with a recollection of the original association. The term was coined by the Wagnerian scholar Hans von Wolzogen.Learn more about leitmotif
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Hey I appreciate the help thank you
Answer:
60 degrees
Step-by-step explanation:
The sum of the interior angles of a triangle are 180. The bottom triangle give you two of the angle measurements (43 and 35) Take 180 - 43 -35 = 102. Angle E is 102. Vertical angles are congruent so that mean that we can use that to find angle a. Again, the sum of the interior angles adds up to 180. 180 - 102 - 18 gives us the measurement of angle a (60)
Suppose that f'(4) = 3 , g'(4) = 7 , g(4) = 4 and g(x) not= to 4 for xnot= to 4 . then cmpute lim xgose to 4 f(g(x))/x-4-f(4)/x-4
It looks like the limit you want to compute is
[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]
Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that
[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]
By the chain rule,
[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]
Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.
I don't understand any recursive sequences please help explain so
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct?
A).Both the domain and range of the transformed function are the same as those of the parent function.
B).Neither the domain nor the range of the transformed function are the same as those of the parent function.
c).The range of the transformed function is the same as the parent function, but the domains of the functions are different.
D).The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.
How to interpret reflection of a function?We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;
|-x| = x
Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|
Thus, from the graph, we get;
Domain of both functions is the set of all real numbers.
Range of both functions is the set {y|y ≥ 0}
Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.
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In total, 2 baseballs and 3 footballs cost $67. a football is $4 more than 3 times the cost of a baseball. find the cost of a baseball
The cost of the Baseball is $5.
Lets take football cost as "x"
And taking baseball cost as "y"
According to given conditions,
2y + 3x = 67
x= 3y + 4
Lets put the values of x in equation (1):
2y + 3 (3y+4) = 67
=> 2y + 9y + 12 = 67
=> 11y = 55
y = 5
x = 3(5) + 4
x = 19
Hence the cost of the Baseball is $5.
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Which system models this situation? y = 26x and y = 8,400(x-500)2 15,900 y = 26x and y = -0.030(x-500)2 15,900 y = x/26 and y = -0.030(x-500)2 15,900 y = x/26 and y =8,400(x-500)2 15,900
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
According to the statement
we have given that Vertex
(h,k) = (500, 15900)
And One of the points on the graph
(x,y) = (0,8400)
FIRST PART: we have to find the quadratic function
We can find the quadratic function by parabola's equation formula
y = a (x - h)² + k -(1)
Input the numbers to the formula, to find the value of a
y = a (x - h)² + k
8400 = a(0 - 500)² + 15900
8400 = a (500)² + 15900
8400 = 250000a + 15900
-250000a = 15900 - 8400
-250000a = 7500
a = 7500/-250000
a = 0.03
Now,
Submit a to the formula (1)
y = a (x - h)² + k
y = 0.03 (x - 500)² + 15900
this is the quadratic equation.
SECOND PART: Find the linear function
the total cost = cost each helmet × the number of helmet
y = 26x
So,
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
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Disclaimer: This question was incomplete. Please find the full content below.
Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)
x= number of helmets
y = amount in dollars
Which system models this situation?
a) y = 26x and y = 8,400(x-500)2+15,900
b) y = 26x and y = -0.030(x-500)2+15,900
c) y = x/26 and y = -0.030(x-500)2+15,900
d) y = x/26 and y =8,400(x-500)2+15,900
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Answer:
B. y = 26x and y = -0.030(x-500)2+15,900
Step-by-step explanation:
the area of a rectangle is 344in²; if the length is 78in, find the width and perimeter of the rectangle
what is the width and perimeter
7. Find the equation of the line passing through the
points P(-2,7) Q(2,-3)
Answer: y=[tex]-\frac{5}{2} x+2[/tex]
Step-by-step explanation:
Use the equation of the line format: y = mx + b
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-3-(7)}{2-(-2)}[/tex]
[tex]m=\frac{-10}{4}[/tex]
simplified
[tex]m=\frac{-5}{2}[/tex]
in order to find B:
[tex]y = -(\frac{5}{2}) *(-2)+b[/tex]
Insert value of y:
[tex]7 = (-\frac{5}{2} ) * (-2) +b[/tex]
Rewrite:
[tex]-\frac{5}{2} * -2 - b=7[/tex]
Cancel the common factor of 2:
[tex]-5 * -1 +b = 7[/tex]
Multiply -5 by -1:
[tex]5 + b= 7[/tex]
Subtract 5 from both sides:
[tex]b = 7-5\\b=2[/tex]
Now substitute values of m, and the final answer is:
[tex]y = -\frac{5}{2}x + 2[/tex]
One factor of the polynomial 3x3 + 20x2 - 21x + 88 is (x + 8). what is the other factor of the polynomial? (note: use long division.)
oa (3x2 - 4x+11)
b. (3x - 4x)
c. (3x2 +11)
d. (3x2 + 4x - 11)
The other factor of the polynomial is a. 3x2-4x+11
Given polynomial is 3x3 + 20x2 - 21x + 88 and the factor is (x+8)
We need to find another factor using long division method
So,
We will divide the polynomial by the factor to find the another factor
Therefore,
[tex]\sqrt[x+8]{3x^3+20x^2-21x+88}[/tex]
Now calculating
First multiplying [tex]3x^2[/tex] with (x+8) so , [tex]3x^2[/tex] will be in the quotient
We get [tex]3x^3+24x^2[/tex]
simplifying the calculation for [tex]3x^3+20x^2[/tex] and [tex]3x^3+24x^2[/tex]
We get the remainder is [tex]-4x^2-21x+88[/tex]
Second we will multiply -4x with (x+8) Where -4x will be in the quotient
We get [tex]-4x^2-32x[/tex] and then we will simplify the equation
We get 11x +88 as a remainder
The quotient we get is [tex]3x^2-4x[/tex]
Third we will multiply +11 with (x+8) Where +11 will be in the quotient
we get 11x+88
Simplifying the equation we get the remainder 0
So the quotient we get is (3x2 - 4x+11)
Hence the another factor of the polynomial is (3x2 - 4x+11)
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The polynomial equation x^4 + x^3 + x^2 + x + 1 = 0 has zero positive real roots. Please select the best answer from the choices provided T F
There are zero positive real roots for the given polynomial equation [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]. This is explained by Descarte's rule of signs. So, the best choice is T (true).
What is Descarte's rule of signs?Descarte's rule of signs tells about the number of positive real roots and negative real roots.The number of changes in signs of the coefficients of the terms of the given polynomial f(x) gives the positive real zeros of the polynomial.The number of changes in signs of the coefficients of the terms of the given polynomial when f(-x) gives the negative real zeros of the polynomial.Calculation:The given polynomial equation is [tex]x^4 + x^3 + x^2 + x + 1 = 0[/tex]
On applying Descarte's rule of signs,
[tex]f(x)=x^4 + x^3 + x^2 + x + 1[/tex]
Since there are no changes in the signs of the coefficients of any of the terms in the above polynomial, the polynomial has no positive real roots.
[tex]f(-x)=(-x)^4+(-x)^3+(-x)^2+(-x)+1\\ = x^4-x^3+x^2-x+1[/tex]
Since there are four changes in the signs of the coefficients of the terms of the given polynomial when f(-x), the polynomial has 4 negative real roots.
Therefore, the given polynomial equation has zero positive real roots. So, the correct choice is T(true).
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Devika buys 30 notebooks and 15 pens. Each book costs Rs40 and that of each pen is Rs15. Find out the total amount she spent.
Answer:
1425
Step-by-step explanation:
Each notebook costs 40, if she buys 30 you can find the total price of notebooks by multiplying the two numbers:
[tex]40*20=1200[/tex]
Each pen costs 15, the same process can be used, multiply price by quantity:
[tex]15*15=225[/tex]
Now just sum the two numbers to find the final price:
1425
Answer:
Step-by-step explanation:
30*40+15*15=
1200+625=
Rs1625
hope this helps
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using HL Theorem.
Question 2
1) [tex]\overline{PR} \perp \overline{QS}[/tex], [tex]\overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ[/tex] and [tex]\angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ[/tex] and [tex]\triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}[/tex], [tex]\overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD[/tex] and [tex]\triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
6.
Write
√18+10
√2
in the form a+b√√3 where a and b are integers.
Answer:
3+10 square root of 2
Step-by-step explanation:
[tex](3 + 10) \sqrt{2} [/tex]
Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Relations and Functions” Below is an example of this.
——————————————————————
Example :
Is the set of ordered pairs below a function? Yes or no, explain your reasoning.
{(4,6),(10,-2),(13,7),(15,8),(10,11)}
——————————————————————
2. Answer each question and show a brief step by step process on how you got the answer to each of your questions.
As per definition
In. a function every domain has an unique range of it
f(x)=yHere
f(4)=6f(10)=-2f(13)=7d(15)=8f(10)=11f(10) has two corresponding values hence it's not a function
John's dad is 30 years old than john. if john were three times ad old as he is now,he would still be younger than his dad. what is the oldest that john could be right now
john could be right now 45
What is word problem in math?
A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."
According to the question:
John's dad is 30 years old than john .In essence, x = y -30 .................equation 1And
john were three times ad old as he is now.y=3xSolution for the above equation:
[tex]x=y-30, y=3 x \quad\\ \quad x=15, y=45[/tex]
steps:
[tex]x=y-30 \\y=3 x[/tex]
Substitute :[tex]$y=3 x$[/tex]
[tex][x=3 x-30][/tex]
[tex]for $$x=3 x-30: \quad x=15[/tex]
For [tex]$y=3 x$[/tex]
Substitute: [tex]$x=15$[/tex]
[tex]y=3 \cdot 15[/tex]
Simplify:
[tex]y=45[/tex]
The solutions to the system of equations are: [tex]$x=15, y=45$[/tex]
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A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working
19 sweets are lefted.
Lets simplify the problem,
Maximum no. of bag filled by 4275 sweets
Through Simple Division we get,
4275/28 ~=152
Therefore , there is 4256 sweets in 152 bags
Therefore, 4275-4256=19 sweets are left
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When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 2 or a 3?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answer:
C
Step-by-step explanation:
There are 6 outcomes and you are seeking 2 of them.
2/6 or 1/3 1:3
How to find the answers?
The computation shows that the value of blue which is represented by x is 12.
How to calculate the value?From the information given, it was stated that 30 people were in the kindergarten.
Green = 10
Red = 8
Blue (x) = 30 - (10 + 8)
= 30 - 18
= 12
Since the teacher want to paint the class with the most favorite color, the appropriate color to use will be blue.
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Help me with this please
Answer:
Step-by-step explanation:
HELP PLEASE!)
A square pyramid has surface that is covered in dark glass. The sides of the pyramid are 456 feet in length. The slant height of the pyramid is 185 feet.
Find the lateral surface area to determine the square feet of glass needed to cover the surface of the pyramid.
Answer choices
376,656 ft^2
42,180 ft^2
337,440 ft ^2
168,720 ft^2
Select the correct answer from the drop-down menu.
Jaden and his family are using a map to drive down to Napa Valley. On the map, the distance is given by the equation c = 1.3m, where c is the number of centimeters on the map and m is the corresponding real-world distance in miles.
If they cover a distance of 18 miles, that would mean a distance of
centimeters on the map.
Answer:
13.846153846
Step-by-step explanation:
Its easy Just 18:1.3=13.846153846
Can someone please help me with this similar area question? I have the answer but I’m not sure how to get to it. Will make brainliest!
Step-by-step explanation:
well there is a very simple point that you have mistaken tho:
484cm², 25cm²
Areas are defined in square cm but the radius is in cm
so:
[tex] \sqrt{ \frac{484 {cm}^{2} }{25 {cm}^{2} } } = \frac{7.92}{r} = = = > 4.4 = \frac{7.92cm}{x} = = > x = \frac{7.92cm}{4.4} = x = 1.8cm[/tex]
and there you go
Very much appreciated!!!
Answer:
80
Step-by-step explanation:
The sum of the interior angles of a triangle is 180. Subtract out the 2 angles that you know.
180 - 70 - 30 = 80
I dont understand:
let CAN be a right triangle with angle C being right angle, side c is 26 cm and side n is 6 cm determine the perimeter of the triangle CAN correct to one decimal enter numerical value only
maybe is my bad english but I dont get it someone can please help?
Using the Pythagorean Theorem, the perimeter of the triangle is of 58.7 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
From your description, I will suppose that the legs are of 6 cm and 26 cm, hence the hypotenuse is:
[tex]h^2 = 6^2 + 26^2[/tex]
[tex]h = \sqrt{6^2 + 26^2}[/tex]
h = 26.7.
The perimeter is the sum of the lengths of the three sides, hence:
P = 26.7 + 26 + 6 = 58.7 cm.
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can someone help me with this thanks
The length of the brace required is 4.3m
What is sine rule?
In a ΔABC a, b and c are the sides and A, B and C are angles then,
[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
We can find the length, l as shown below:
Let AB=3m, BC=2m and AC=l
Let ∠A=25°
So, in ΔABC
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]
[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]
[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]
∠C=39.34°
∠A+∠B+∠C=180°
∠B=180°-25°-39.34°
∠B=115.66°
[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]
[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]
[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]
l=4.2659
Rounding to nearest tenth of meter.
l=4.3m
Hence, the length of the brace required is 4.3m
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A river flows at 2m/s . Juan's boat can travel twice as fast down the river as it can go up the river. how fast the boat go in still water?
Using proportions, it is found that the boat can go 6 m/s in still water.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
Down the river, the speed is v + 2.Up the river, the speed is v - 2.He goes twice as fast down the river, hence:
v + 2 = 2(v - 2).
v + 2 = 2v - 4
2v - v = 2 + 4
v = 6.
The boat can go 6 m/s in still water.
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Beau Thai has a rectangular mirror with a length of 6 inches and a width of 10 inches.
a) How much ribbon could Beau wrap around the outside of the mirror?
b) What is the area of Beau Thai's mirror?
a. Amount needed to wrap the outside of the rectangular mirror around = 32 inches.
b. Area of the Beau Thai's rectangular mirror around = 60 square inches.
What is the Area of a Rectangle?Area of a rectangle = (l)(w), where l is the length and w is the width of the rectangle.
What is the Perimeter of a Rectangle?Perimeter of a rectangle = 2(l + w), where l is the length and w is the width of the rectangle.
a. The amount of ribbon that can be used to wrap the outside of the mirror around can be determined by using the formula for the perimeter of a rectangle.
Length of rectangular mirror = 6 inches
Width of rectangular mirror = 10 inches
Perimeter = 2(6 + 10)
Perimeter = 2(16)
Perimeter = 32 inches
Amount needed to wrap the outside of the rectangular mirror around = 32 inches.
b. The area of Beau Thai's rectangular mirror can be determined by using the formula for the area of a rectangle.
Length of rectangular mirror = 6 inches
Width of rectangular mirror = 10 inches
Area = (6)(10)
Area = 60 square inches
Area of the Beau Thai's rectangular mirror around = 60 square inches.
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