The value of the numerator of the calculation of the variance= 258
and Variance= 51.6
Step-by-step explanation:We know that in order to calculate the variance we need to follow following steps:
First calculate mean.Then subtract each of the data points from means and square the difference quantity.Lastly calculate the mean of these squared quantity.The data points are:
90, 75, 72, 88, 85
The mean of these data points are:
[tex]Mean=\dfrac{90+75+72+88+85}{5}\\\\\\Mean=\dfrac{410}{5}\\\\\\Mean=82[/tex]
Now on finding the difference terms i.e.
90-82=8
75-82= -7
72-82= -10
88-82=6
and 85-82=3
The square of these difference term is:
8²=64
(-7)²=49
(-10)²=100
6²=36
and 3²=9
Hence, the mean of these squared quantity i.e. Variance is:
[tex]Variance=\dfrac{64+49+100+36+9}{5}\\\\\\Variance=\dfrac{258}{5}\\\\\\Variance=51.6[/tex]
Gth of a square tile is 8.0cm what is the approximatenlength of the tile in inches
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer: [tex]4y=-3x-7[/tex]
Step-by-step explanation:
The equation of a line passing through (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
The equation of a line passing through (5, -2) and (-3, 4) is given by :-
[tex](y-(-2))=\dfrac{4-(-2)}{-3-5}(x-5)\\\\\Rightarrow\ y+2=\dfrac{6}{-8}(x-5)\\\\\Rightarrow\ y+2=\dfrac{-3}{4}(x-5)\\\\\Rightarrow\ 4(y+2)=-3(x-5)\\\\\Rightarrow\ 4y+8=-3x+15\\\\\Rightarrow\ 4y=-3x-7[/tex]
Et f(x) = 9x − 2 and g(x) = −x + 3. find f(g(x)). −9x − 2 −9x + 5 −9x + 25 −9x + 27
Answer:
its a on edg
Step-by-step explanation:
im 100%
Evaluate the function at the given value of the independent variable and simplify f(x)= x^2 + 1
Determine if the statement is always, sometimes, or never true:
An equilateral triangle is a right triangle.
always
sometimes
never
Answer:
never
Step-by-step explanation:
To Find :An equilateral triangle is a right triangle.
1. always
2.sometimes
3.never
Solution :
Definition of equilateral triangles: a triangle having all sides equal in length
Since all sides are equal so by property of triangle (angle opposite to equal sides are equal ) so, all angles are equal .
If equilateral triangle is right angle then one of its angle is of 90°
And in equilatera triangle all angles are equal so all angles must be of 90°
We know that triangle sum property is : Sum of all angles of triangle is equal to 180°
So, 90°+90°+ 90° =180°
⇒270°≠180°
since this violates the angle sum property of triangle .
Thus an equilateral triangle can never be a right triangle
Answer:
NEVER
Step-by-step explanation:
A 0.5-kg ball accelerated at 50 m/s2 . What force was applied?
What is the sum of 2.5 × 10^4 and 3.4 × 10^4?
A segment has endpoints F and H . What are two names for the segment?
What is the conclusion in this conditional statement?
If a square has a perimeter of 8 units, then its sides have a length of 2 units each.
the square has a perimeter of 8 units
the sides of the square have a length of 2 units each
Submit
The conclusion in the given conditional statement is that the sides of the square have a length of 2 units each. This is deduced from the formula for the perimeter of a square (P = 4 × side length), and the given perimeter of 8 units.
Explanation:The conclusion in the conditional statement "If a square has a perimeter of 8 units, then its sides have a length of 2 units each" is the sides of the square have a length of 2 units each.
In a conditional statement, the "if" part is known as the hypothesis and the "then" part is the conclusion. Given that a square's perimeter is the sum of the lengths of all four sides, we can show this through an equation: P = 4 × s, where P represents the perimeter and s the length of one side. Since the perimeter is given as 8 units, we can solve for s by dividing the perimeter by 4: 8 units = 4 × s, which simplifies to s = 2 units. Therefore, each side of the square must be 2 units long.
Final answer:
The conclusion in this conditional statement is that the sides of the square have a length of 2 units each.
Explanation:
The conclusion in this conditional statement is:
The sides of the square have a length of 2 units each.
In a conditional statement of the form 'if A, then B', the conclusion (B) is the statement that follows 'then'. In this case, the conclusion states that the sides of the square have a length of 2 units each.
A movie theater sold a total of 390 adult and child tickets on a certain day. The theater sold 2.25 times as many adult tickets as child tickets. Each adult ticket cost $7 and each child ticket cost $3. How much revenue did the theater generate in ticket sales that day?
The Revenue generated by theater is $2,250.
What is simplification?Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
It is possible to simplify mathematical formulas by merging and grouping related terms. This makes it easy to understand and decipher the puzzle.
Given total ticket sold = 390
adult ticket + child ticket = 390
and 2.25 times as many adult tickets as child tickets
so adult ticket = 2.25 child tickets
Let child ticket be x
adult ticket = 2.25x
equation will be
2.25x + x = 390
3.25x = 390
x = 120
adult ticket = 390 - 120 = 270
cost of 1 adult ticket = $7
cost of 270 adult ticket = 7 x 270 = $1890
cost of 1 child ticket = $3
cost of 120 child ticket = 3 x 120 = $360
Total revenue = $1890 + $360
Total revenue = $2,250
Hence the total collection of theater is $2,250.
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To make the bowling team. Jacques needs a three-game average of 160. If he bowled 141 and 162 for the first two games, what score S must be obtained in the third game so that his average is at least 160?
Does adding zero to a number ever change its value? what is this property called?
Please help :)))) ( attachment )
Can anybody help me with this? It's geometry
When one thing is ten times as large as another, it is said to be "an order of magnitude" larger. a hundred times larger is two orders of magnitude. a thousand is three orders of magnitude. by how many orders of magnitude is the empire state building taller than a chair seat?
Sophia used the digits 6, 3, and 8 to write a number less than 6 and greater than 5. Her number has three digits, and the digit in the tenths place is odd. She used each digit only once in the number. What is Sophia's number?
If the highest score in a distribution is x = 16 and the lowest is x = 4, then the range is 12 or 13 points.
a. True
b. False
The range in the given scenario is only 12 points, not 12 or 13 points as mentioned.
False
Range = Highest score - Lowest score
Range = 16 - 4 = 12
Therefore, the range can only be 12 points.
The standard recommendation for fluid needs is 30 ml/kg body weight. parker weighs 67 kg. how many cups of fluid will he need? (give your answer to the nearest tenth. give only the value. do not write the word cup or its abbreviation.)
A class has 11 boys and 9 girls in it. what percent of the class are boys
Answer: the answer is C 55%
Hope this helps you
1. Graph the system of inequalities.
–2x + 3y ≥ –12
x + y < 3
how do i graph on a word doc?
see attached picture of how graph should look.
search through word for a graph icon, you should be able to do this in Word.
The area of this parallelogram is 24 square units the base is 8 units what is the height of the figure
The floor of a conference hall can be covered completly with tiles.Its length is 36ft. longer than its width.The area of the floor is less than 2040square ft.How would you represent the with of the floor?How about its lenght?What mathematical sentence would represent the given situation?What are the possible dimensions of the floor?How about the possible areas of the floor?Would it be realistic for the floor to have an area of 144sq.ft?Explain your answer.
W<30; The width of the floor will be less than 30feet
The possible area of the floor is 1885 sq. ftSince 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft
The formula for calculating the area of the conference floor is expressed as:
A = LW
L is the length
W is the width
If the length is 36ft. longer than its width, hence;
L = W+36
Since the area of the floor is less than 2040 square feet, hence;
A < 2040
LW < 2040
(W+36)W < 2040
W² + 38W < 2040
W² + 38W - 2040 < 0
W² + 68W - 30W - 2040 < 0
W(W+68)- 30(W+68)< 0
(W-30)(W+68) < 0
W - 30 < 0 and W < -68
W < 30
Since the width cannot be negative, hence the width of the floor will be less than 30feet
Since L = 36 + W
L < 36 + 30
L < 66feet
The length of the floor will be less than 66feet
The possible dimensions area 29feet by 65feet since the width is less than 30 and the length is less than 66feet.
Get the possible area:
Possible area = 29 × 65
Possible area = 1885feet²
Since 144 sq.ft ≠ 1885feet², hence it would not be realistic for the floor to have an area of 144sq.ft
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Maria says that 6.25 os 1/100 the value od 625.Wriye an explanation to support Maria's statement.You can use equations or models in your explanation.
what are rational numbers
A coin is tossed 6 times. what is the probability of getting at least one head? express your answer as a fraction or a decimal number rounded to four decimal places.
Final answer:
The probability of getting at least one head in six coin tosses is 1 minus the probability of getting tails on all tosses, resulting in a probability of 98.44% when rounded to four decimal places.
Explanation:
The question is about calculating the probability of getting at least one head when a coin is tossed six times. Rather than calculating the probability of at least one head directly, it's simpler to calculate the probability of the opposite event—getting no heads—which is the same as getting tails on all six tosses. Since the probability of flipping a tail on each toss is 0.5, the probability of flipping six tails in a row is (0.5)⁶, which equals 0.015625. Therefore, the probability of getting at least one head is 1 minus the probability of getting no heads, which is 1 - 0.015625, resulting in 0.984375 or 98.44% when rounded to four decimal places.
S=p-0.2t solve for p
Answer:
The required equation is [tex]S+0.2t=p[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]S=p-0.2t[/tex]
We need to solve the equation for p.
Isolate the variable as shown.
Add 0.2t from both sides.
[tex]S+0.2t=p-0.2t+0.2t[/tex]
[tex]S+0.2t=p[/tex]
Hence, the required equation is [tex]S+0.2t=p[/tex]
Planes X and Y are perpendicular. Points A, E, F, and G are points only in plane X. Points R and S are points in both planes X and Y. Lines EA and FG are parallel.
Based on this information, which lines could be perpendicular to RS? Check all that apply.
EA,ER,EF,FG,FS
Answer:
Step-by-step explanation:
How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year, compounded quarterly?
Compound interest formula
[tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
Where
A= Future value
P =
the Principal (the initial amount of money)
r = annual interest rate
t = time
n= number of times compounded in one tA= 30 000
P =20 000
r = 15%=0.15
time = t = ?
n= 4What is the solution of 7<5-2x<17
What is 60% of 7?????
60% = 0.60
7*0.6 = 4.2