Answer:
100, 120
Step-by-step explanation:
The mean of the given data is 500/4, or 125.
If a score of 0 were added to this data, the mean would be smaller, because we'd have to divide the five scores by 5. The mean would now be 100.
The median of the given data is the average of the middle two scores, that is, of 120 and 130. It's 125.
If we were to add the score of 0 to the four data points, obtaining
0, 100, 120, 130, 150,
the median would be the middle number: 120.
Mean is the average of the data set and mode is the middle terms or average of the middle terms of the data set.
Given information-
The given data consists the values 100,120,130,150.
Total number of values is four.
MeanMean is the average of the given data.
The mean of the given data can be calculated as,
[tex]m=\dfrac{100+120+130+150}{4} [/tex]
[tex]m=\dfrac{500}{4} [/tex]
[tex]m=125[/tex]
MediumFor even terms the medium is the average of the middle terms.
The medium of the given data can be calculates as,
[tex]M=\dfrac{120+130}{2} [/tex]
[tex]M=125[/tex]
Adding a score of 0.
The data consists of the values will be 0,100,120,130,150.
Total number of values is five.
MeanThe mean of the given data can be calculated as,
[tex]m=\dfrac{0+100+120+130+150}{5} [/tex]
[tex]m=\dfrac{500}{5} [/tex]
[tex]m=100[/tex]
MediumMedium for the odd terms is equal to the middle terms.
The medium of the given data can be calculates as,
For the
[tex]M=120[/tex]
Thus adding a score of 0 the mean of the given data is reduced with number 25 and the mode reduced with number 5.
Learn more about the mean and medium here;
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In ®A shown below, radius AB is perpendicular to chord XY at point C. If XY=24 and AC=5 cm, what is the radius of the circle?
ANSWER
B. 13cm
EXPLANATION
The radius of the circle becomes the hypotenuse of the right triangle formed.
We can use the Pythagoras Theorem to obtain,
AC²+CY²=r²
This implies that,
r²=5²+12²
r²=25+144
r²=169
Take positive square root to get;
r=√169
r=13
AB and AC are two equal chord of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.
OA is the bisector of ∠BAC.
Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.
P divides BC in the ratio 6:6=1:1.
P is mid-point of BC.
OP ⊥ BC.
In △ ABP, by pythagoras theorem,
AB2=AP2+BP2
BP2=36−AP2 ....(1)
In △ OBP, we have
OB2=OP2+BP2
52=(5−AP)2+BP2
BP2=25−(5−AP)2 .....(2)
From 1 & 2, we get,
36−AP2=25−(5−AP)2
36=10AP
AP=3.6cm
Substitute in equation 1,
BP2=36−(3.6)2=23.04
BP=4.8cm
BC=2×4.8=9.6cm
(6Q) Find the domain and range.
Answer: Option a.
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
We have the function [tex]f(x) = 2x + cosx[/tex]
Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]
The domain and range of h(x) are all real numbers
The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]
Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].
Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)
The range of f(x) will be equal to the union of the range of g(x) and h(x)
Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)
Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE!!
Answer:
V = 115.3 ft³
Step-by-step explanation:
The left part of the figure shows a cube of side length 4.2 ft. The volume of a cube is V = s³, where s is the side length. Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.
The volume of a pyramid is V = (1/3)(base area)(height).
Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.
Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or
V = 115.3 ft³ after rounding up to the nearest tenth.
The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
What are Three Dimensional Figures ?Those figures that required x,y and z axis for their representation are three dimensional figures.
They have length , breadth and height.
All the object that we see around us can be categorized into Three Dimensional Figure.
In the given figure
It can be seen that it consists of a cube and a square pyramid
To determine the volume we have to determine the volume of each figure and then add
Volume of a cube = side * side * side
Side of the cube = 4.2 ft.
Substituting the values
Volume of cube = 4.2 * 4.2 * 4.2
Volume of cube = 74.088 cu.ft
Volume of a square pyramid is given by
(1/3) * a² * h
a is the area of the base
area of the base = area of the square = side * side
Area of the base = 4.2 * 4.2
Area of the base = 17.64 sq.ft
Height of the pyramid = 7 ft.
Volume of square pyramid = (1/3)* 17.64 *7
Volume of a square pyramid = 41.16 cu.ft
Total volume = 74.088 + 41.16
Total Volume = 115.2 cu.ft
Therefore , The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
To know more about Three Dimensional Figures
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Sophie Ruth is eating a 505050-gram chocolate bar which contains 30\%30%30, percent cocoa. How many grams of cocoa are in the chocolate bar?
Answer:
15 g
Step-by-step explanation:
30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g
Answer:
15g
Step-by-step explanation:
In a bag there are 5 red marbles, 10 blue marbles, and 15 green marbles. What is the probability that you will draw a blue marble?
1/2
1/3
2/3
3/4
probability of drawing a blue marble is 1/3
A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
4046.56 cm3
Step-by-step explanation:
The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.
Your volume will be [tex]5 * \frac {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]
Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For Safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? show your work
Answer:
No, it is not safe
Answer:
Hello!
The answer is no, he will not be safe. I had a similar problem on a test and got the answer correct. The only difference was they used slightly different numbers, so I am pretty sure this is correct. I hope this helps!
Step-by-step explanation:
Okay, so you are looking for x.
sin x= [tex]\frac{16.5}{17}[/tex]
x=[tex]sin^{-1}[/tex]([tex]\frac{16.5}{17}[/tex])
x≈76.07
76.07>70
Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square. Also find the area of the square.
Answer:
the point r would be located at (4,3)
Step-by-step explanation:
granted that the quadralaterel is a square that would mean that all side lengths are equal and the distance between points x and q is 3 meaning that the same would have to be said about the distance between s and r
PLEASE HELP ME OUT :) Independent or Dependent?
Also, is there an easier way to determine if these are independent or dependent other than working out the entire problem? (Not trying to be lazy. My school website uses common core learning which explains each problem in, seemingly, the most difficult way possible for most different types of algebra and geometry)
Answer:
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
Step-by-step explanation:
Two events A and B are independent if the occurrence of A does not affect the probability of B.
On the other hand The probability of A given B is defined as:
[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]
When two events are independent then:
[tex]P (A\ and\ B) = P (A) * P (B)[/tex]
So if the two events A and B are independent this means that:
[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]
[tex]P (A | B) = P (A)[/tex]
Which makes sense because if the events are independent then the probability of A not being affected by B.
So to solve this problem identify in what cases
[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]
When this happens those events are independent
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
The pie store is having a 20% , percent off sale on all of its pies. If the pie you want regularly costs $18 dollar sign, 18, how much would you save with the discount?
20% off, means that 20% of the regular price is how much you would save.
Multiply the original price by 20%
18 x 0.20 = 3.6
The discount is $3.60
Investigation Circles: Investigation 2
I need help with the worksheet
Explanation:
1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.
"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."
__
2. We know from the first question that ...
circumference/diameter = π
And we know that ...
diameter = 2·radius
Then the following are true:
A. circumference = π · diameter
B. circumference = (2·radius) · π
__
3. The expressions in order evaluate to approximately ...
4.0, 3.45, 3.31, 3.24
Of these, the last is closest to pi (3.14....). The appropriate choice is ...
D. (10·5)/15.4
__
4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.
Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 220 yards toward the mountain. The angle of elevation of the top is now 27°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.
Answer:
559.2 yards.
Step-by-step explanation:
Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.
Then we have the equations:
tan 27 = x/y
tan 23 = x / (220 + y)
From the first equation y = x/ tan27 so substituting in the second one we have:
tan 23 = x / (220 + x / tan 27)
Cross multiply:
x = 220 tan23 + x tan 23 / tan 27
x = 93.384 + 0.833 x
x - 0.833x = 93.384
x = 93.384 / 0.167
x = 559.2 yards to 1 dec place (answer).
Please please help me
Answer: 5 Vertices
Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.
Please answer this correctly
Answer:8462
Step-by-step explanation:
Answer:
8862 feet
Explanation:
The formula for circumference is C=pi*diameter. So, by substitution we can use 26586=(3)d and solve by dividing 26586 by 3 which gives us d=8862 feet.
Frank and his family are going to the grand opening of a circus there is a special price on tickets this weekend tickets cost 36 each this is a 60% of the cost of a regular price ticket. What is the cost of a regular price ticket?
Answer:
60
Step-by-step explanation:
(This is not how teachers usually teach you)
First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.
Answer:
The cost of a regular price ticket is $60.Step-by-step explanation:
Givens
Tickets cost $36 each, which represents 60% of the regular price.To find the regular price for tickets, we can use the rule of three.
If $36 represents 60%, how much would represents 100%?
[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]
Therefore, the cost of a regular price ticket is $60.
The equation of a circle is x2+y2−12x+6y+20=0 .
What is the radius of the circle?
r = ?
Answer:
The radius is r=5 units
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
we have
[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]
therefore
The center is the point (6,-3) and the radius is r=5 units
A stove costs $695 will be on sale next week for 20% off its regular price. What is the amount of savings
Answer:
It would be 139$
Step-by-step explanation:
In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.
Can someone help please
Answer:
62 Sunday papers were sold
Step-by-step explanation:
Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:
1.50 · x + 0.75 · (x/2) = 116.25
Multiplying by 2, this becomes ...
3.00x +0.75x = 232.50
3.75x = 232.50
Dividing by the coefficient of x gives ...
232.50/3.75 = x = 62
The number of Sunday newspapers sold is 62.
What equation/thing is happening to this number to get this solution? My book is just telling me "use a calculator" but it doesn't explain it any further. Please help!
Answer:
Use the square root function on your calculator
Step-by-step explanation:
Look at the third line down, where is says that 936 = AD^2. If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function. After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator. The square root of 936 is 30.59417
Find the area of the triangle.
Answer: 118.3 m^2
Step-by-step explanation:
Use Heron's formula: √s(s-a)(s-b)(s-c)
s= a+b+c/2
13+18.2+22.3/2 = 26.75
√26.75(26.75-13)(26.75-18.2)(26.75-22.3)
√26.75(13.75)(8.55)(4.45)
√13994.34609
118.297701 = 118.3 m^2
What is the area of triangle ABC? Round your final answer to the nearest cm.
Answer:
A = 21.65 cm squared
Step-by-step explanation:
The basic area formula for a triangle is
[tex]A= \frac{1}{2}bh[/tex]
We have our base as 5, so we can find the height using right triangle trig. Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base. Using the tangent ratio to find side BC:
[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to
5 tan(60) = x so
x = 8.66
Filling in for the area:
[tex]A= \frac{1}{2}(5)(8.66)[/tex] so
A = 21.65 cm squared
Please please help me..
The yellow and orange triangle is AA
It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.
Answer:
AA
Step-by-step explanation:
For the 2 triangles to be similar we require 2 corresponding angles to be congruent.
There are 2 angles of measure 30°
If we consider the yellow triangle the the third angle is
180° - ( 41 + 30)° = 180° - 71 = 109°
The 2 triangles have therefore 2 corresponding congruent angles
Hence the triangles are similar by the postulate AA
Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.
His answer is f(x) = (
)2 – 5.
Hm, it seems like his answer is off. The image is what I got.
Answers:
X+3
Step-by-step explanation:
I got it right
Sasha has a fever of 103°F. What is Sasha’s fever in degrees Celsius?
32°C
39.4°C
66.9°C
71°C
39.4 degrees Celsius
Hope this helps :)
Answer:
39.4°C
Step-by-step explanation:
The equation for fahrenheit to celsius is
(°F − 32) × 5/9 = °C
With our variable of 103 plugged in it is
(103°F − 32) × 5/9 = 39.444°C
Therefore, her fever is 39.4°c
The range of which function includes –4?
Answer:
[tex]y=\sqrt{x} -5[/tex]
Answer:
The function [tex]f(x)=\sqrt{x-5}[/tex]
Step-by-step explanation:
The Range of any function is complete set of all possible resulting values of the dependent variable , after substituting the domain.
so, the function [tex]f(x)=\sqrt{x-5}[/tex] has range [tex]f(x)$\geq$ -5[/tex]
This includes - 4 .
Hence, the function is [tex]f(x)=\sqrt{x-5}[/tex] .
Solve x^2 +5x-10=0. How do you solve this
Answer:
(-5 +/- sqrt(65))/2
Step-by-step explanation:
To solve this, we can use the quadratic formula!
So,
x = (-b +/- sqrt(b^2-4ac))/2a
x = (-5 +/- sqrt(25+40))/2
x = (-5 +/- sqrt(65))/2
So (-5 +/- sqrt(65))/2 is our answer.
Approximately how much water does the average american use every day?
Answer: Estimates vary, but each person uses about 80-100 gallons of water per day
BASIC MATH
Paul uses the expression 4.2 x 12.3 x 14.6 to determine the cost of tiling the floor of a room that measures 12.3 feet by 14.6 feet; each square foot of tile costs $4.20. How many decimal places will be in Paul’s final answer?
A. one
B. three
C. five
D. eight
B. Three. It is three because there is one decimal place in each factor.
Answer:
B. Three.
Explanation:
Three because there is one decimal place in each factor and there are 3 factors.
I need help
A rectangular shelf has a perimeter of 46 inches. Its area is 76 square inches. What are the dimensions of the shelf?
Answer:
19 in × 4 inStep-by-step explanation:
l - length
w - width
The formula of a perimeter of a rectangle: P = 2(l + w)
The formula of an area of a rectangle: A = lw
We have P = 46in and A = 76in² Substitute:
(1) 2(l + w) = 46
(2) lw = 76
2(l + w) = 46 divide both sides by 2
l + w = 23 subtract w from both sides
l = 23 - w
subtitute it to (2):
(23 - w)w = 76 use the distributive property
23w - w² = 76 subtract 76 from both sides
-w² + 23w - 76 = 0 change the signs
w² - 23w + 76 = 0
w² - 4w - 19w + 76 = 0
w(w - 4) - 19(w - 4) = 0
(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0
w - 4 = 0 add 4 to both sides
w = 4
w - 19 = 0 add 19 to both sides
w = 19
Put the values of w to (1):
l = 23 - 4 = 19 or l = 23 - 19 = 4
I need help getting started please
Check the picture below.
so, the triangular prism is really 2 triangles and 3 rectangles stacked up to each other at the edges. Let's simply get the area of each shape and sum them up, and that's the area of the prism.
[tex]\bf \stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{6})(\stackrel{height}{5.2}) \right]}+\stackrel{\textit{right-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{left-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{base rectangle}}{(8\cdot 6)} \\\\\\ 31.2+48+48+48\implies 175.2[/tex]
Answer:
The surface area = 175.2 mm²
Step-by-step explanation:
Formula:-
Area of rectangle = lb
Area of triangle = bh/2
It is given a triangular prism.
To find the surface area
Surface area = 3 Rectangle area + 2 triangle area
Rectangle area = 3 * lb
= 3 * 8 * 6
= 144 mm²
Triangle area = 2 * bh/2 = bh
= 6 * 5.2 = 31.2²
Total area = 144 + 31.2 = 175.2 mm²