Rounded to the nearest whole number, the standard deviation of the data is 29.
How do we calculate the standard deviation of data?The following notations and formulas will be used in these calculations:
Mean = (sum of the values) / n
Variance = ((Σ(x - mean)^2) / (n - 1)
Standard deviation = Variance^0.5
Where:
n = number of values = 4
x = each value
Therefore, we have:
Mean = (65 + 75 + 100 + 130) / 4 = 92.50
Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) = 2,525 / 3 = 841.666666666667
Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882
Rounding to the nearest whole number, we have:
Standard deviation = 29
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Answer:
The answer is C. 100
Step-by-step explanation:
A man stands on his balcony, 140 feet above the ground. He looks at the ground, with his sight line forming an angle of
75 with the building, and sees a bus stop. The function d=140 sec 0 models the distance from the man to any object given
his angle of sight 0. How far is the bus stop from the man? Round your answer to the nearest foot.
The bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet
How to determine the distance?The distance function is given as:
d = 140 sec(x)
Where x represents the angle of sight.
In this case,
x = 75
So, we have:
d = 140 sec(75)
Evaluate the product
d = 541
Hence, the bus at an angle of sight of 75 degrees from the man is at a distance of 541 feet
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Which function is a quadratic function?
Op(x) = 2x(x2 +6) +1
O m(x) = 4(x + 3) - 2
1
O f(x) = -8x²(x² − 6) + 1
O h(x) = 3x(x - 2) - 4
Answer:
h(x) = 3x(x - 2) - 4
Step-by-step explanation:
A quadratic function is a polynomial having a degree of 2.
==============================================================
On expanding h(x) :
⇒ h(x) = 3x (x - 2) - 4
⇒ h(x) = 3x² - 6x - 4
=============================================================
Hence, h(x) is a quadratic function.
Answer:
h(x) = 3x(x - 2) - 4
Step by-step explanation
A quadratic function has a degree of 2.
Firstly, we expand h(x):
h(x) = 3x (x - 2) - 4
OR h(x) = 3x squared - 6x - 4
Therefore, it is h(x)
What is the area of the trapezoid shown? The figure is not drawn to scale.
284.31 in.²
303.75 in.²
568.62 in.²
607.5 in.2
Answer:
284.3
Step-by-step explanation:
Trapezoid Formula:
A=a+b/2*h
plug in the numbers
Ms. Stewart teaches three science classes. Her students are freshmen and
sophomores. Her student data are shown in the relative frequency table.
Which statement is false?
The statement that is false is 15% of her students are in biology, the correct option is A.
How to form two-way table?Suppose two dimensions are there, viz X and Y. Some values of X are there as X_1, X_2, ... , X_n and some values of Y are there as Y_1, Y_2, ... , Y_n
List them in title of the rows and left to the columns. There will be n \times k table of values will be formed(excluding titles and totals), such that:
Value(ith row, jth column) = Frequency for intersection of X_i and Y_j (assuming X values are going in rows, and Y values are listed in columns).
Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.
For n = 2, and k = 2, the table would look like:
[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]
where S denotes total of totals, also called total frequency.
n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.
We are given that;
The relative frequency table
Now,
This is because the relative frequency table shows that 0.15 of her students are freshmen in biology and 0.2 of her students are sophomores in biology. Therefore, the total percentage of her students in biology is 0.15 + 0.2 = 0.35, which is 35%, not 15%.
The other statements are true based on the relative frequency table.
Therefore, by the two-way table the answer will be 15% of her students are in biology.
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three consecutive integers such that the smallest and three times the largest is 330 . what is the smallest integer?
Consider the equation:
6x+55=x²
1) Rewrite the equation by completing the square.
Step-by-step explanation:
-x^2+6x+55=0
x^2-6x-55=0
x^2-6x+(3)^2-55-(3)^2=0
(x-3)^2-64=0
Which measure is of an angle that is coterminal with a 425° angle?
425° – (1,000n)°, for any integer n
425° – (840n)°, for any integer n
425° + (960n)°, for any integer n
425° + (1,440n)°, for any integer n
The measure of angle that is coterminal with 425° is 425° + (1440n)°
What are coterminal angles?Coterminal angles are angles in multiples of the angles in standard positions examples(360°).
It is mostly gotten by adding 360° or multiples of 360 to the angle.
One of the unique behavior of coterminal angles is that their sine, cosine and tangent are equal.
Analysis:
From the options, the only one with an addition of 360 or multiples of 360 is 425 + 1440n
If we put n = 1, the coterminal angle gotten is 1865.
if we find the sine of 425°, we get 0.9063 which is same as the sine of 1865°.
In conclusion, the coterminal angle to 425° is 425° + (1440n)°.
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Answer:
B. 425° – (840n)°, for any integer n
DOES the given value make the inequalities true? x + 9 > 21, when x = 15?
Answer:
Yes.
Step-by-step explanation:
When [tex]x=15[/tex],
[tex]x+9=15+9=24 > 21[/tex].
Answer:
Yes this is true
Step-by-step explanation:
24 is greater than 21; which means this statement is always true.
Meril Starts driving at 14 00
What is the mode: 18,21,22,18,19
Answer:
18
Step-by-step explanation:
Mode = modal class (Recurring)
The number/value that appears the most which in this case is 18 because it can be seen twice.
A major river flowing out of the Himalayas
Answer:
The Ganges
Step-by-step explanation:
Answer:
Ganga
Step-by-step explanation:
Ganga is the holy river of IndiaIt has risen from Himalayas.It flows throughout the Ind and falls at Sundarban inside Bay of BangalToni participates in a 10-mile charity walk. For each mile she walks, a sponsor will donate $9 to the charity. The graph represents the function that models the amount of money the sponsor will donate given the number of miles, x, Toni walks. what is the domain of the fuction
The domain of the function when Toni participates in a 10-mile charity walk will be [0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90]
What is a function?It should be noted that a function simply means a relation that's used to express a variable with another variable.
In this case, it should be noted that a domain simply means the set of possible values of the independent variable. The function here is 9x. The domain is all x-values or inputs of a function. Therefore, the domain is depicted above.
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Shane's age is 8 years more than three times Edward's age. Their combined age is 56 years.
How old is Shane?
: The proliferation of the Internet has given rise to a new method of advertising, called spamming, that essentially is a more cost-effective method of the telephone solicitation method known as cold calling. If a company buys three mailing lists with 2,500, 3,500, and 4,000 email addresses respectively and spams them with promotional material, how many potential customers has it reached?
The number of potential customers that the company has reached is 10,000 e--mail addresses.
What is a word problem in mathematics?A word problem is a real-life problem and it can be approached with the use of a mathematical model, interpretation into variables, and arithmetic operations usage.
Given that:
A company buys three mailing lists with 2500, 3500, and 4000 addresses respectively.The number of potential customers that the company has reached is:
= 2500 3500 + 4000 e--mail addresses.
= 10,000 e--mail addresses.
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Please help will give 30 points.
Answer: I think that the answer would be B. This is what i got after doing the work
Horizontal stadia sights. Determine the error in distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight
The error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
What is Tangent (Tanθ)?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
Tan(θ) = Perpendicular/Base
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given the uppermost portion of a that is 3.0m long stadia rod is inclined 14 cm toward the observer, therefore, the angle of inclination, θ can be written as
tan(θ)=0.14/3
θ = 2.672°
Also, the rod intercept is 1.75m, therefore, t the error in distance in the distance is,
tanθ=x/1.75
x = 1.75 tan(θ)
x = 1.75 × tan(2.672°)
x = 0.08167 m = 8.167 cm
Hence, the error in the distance if the uppermost portion of a 3. 0m long stadia rod is inclined 14 cm toward the observer and the rod intercept is 1. 75m on a horizontal sight is 8.167cm.
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Which is the most reasonable estimate of 132% of 48?
5.2
6.5
52
65
Answer:
65
Step-by-step explanation
Just did it on egde
Find the midpoint of the line segment
1) (-2,-4), (10,8)
Answer:
(4, 2)
Step-by-step explanation:
the midpoint of points (x1, y1) and (x2, y2) is ([tex]\frac{x_{1} + x_{2}}{2}[/tex],[tex]\frac{y_{1} + y_{2}}{2}[/tex])
plug in points (-2, -4) and (10, 8) to get ((10+(-2))/2), (8+(-4))/2) = (4, 2)
A family wants to make a 20% downpayment on a house that costs $20,000, which of the amount is the downpayment?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 20000}}{\left( \cfrac{20}{100} \right)20000}\implies 4000\qquad \impliedby downpayment[/tex]
0 x + 12 + x = 18
Solve ?
Answer:
x = 3
Step-by-step explanation:
2x + 12 = 18
2x = 18-12
2x = 6
x = 3
give brainliest please!
hope htis helps :)
Answer:6
Step-by-step explanation:
0x+12+x=18
0x+x=18-12
x=6
Find the length of the third side. If necessary, write in simplest radical form.
[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~~~\text{Hypotenuse}^2=\text{Base}^2 + \text{Perpendicular}^2\\\\\implies 9^2 = \text{Base}^2 + \left(2\sqrt{14} \right)^2\\\\\implies 81 = \text{Base}^2 + 56\\\\\implies \text{Base}^2 = 81-56\\\\\implies \text{Base}^2 = 25\\\\\implies \text{Base} = \sqrt{25}\\\\\implies \text{Base} = 5\\\\\text{The length of the third side is 5 units.}[/tex]
Which of the following expressions is equivalent to the one shown below?
OA. 5.-11
OB. (-11)
14
OC.
(-11)
D. (-11)
145
The expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
Indices expressionGiven the expression as shown below
(-11/15)⁵
This expression means that we are to raise the value -11 and 14 raised to the power of 5 individually as shown:
(-11/15)⁵ = (-11)⁵/(15)⁵
Hence the expression that is equivalent to (-11/15)⁵ is (-11)⁵/(15)⁵
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A website advertises 85 video games for $1969. How much would 160 video games cost at the same unit
price?
Answer:
$3705.60
Step-by-step explanation:
1969/85=23.16
23.16x160=3705.6
Hurry help
If p is true and ~ q is false, then p -> ~ q is ____ false.
-Sometimes
-Always
-Never
Answer:
Never
Step-by-step explanation:
If p is true and ~ q is false, then p -> ~ q is ____ false
This translates to:
true -> true
So it will never be false.
Help ?!!!!!!!!!!?!!!!!!
The answers of the given geometrical shapes are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
what is mensuration?Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.
Analysis:
1. volume of cylinder =π [tex]r^{2}[/tex]h. where r = 6/2 = 3 yard, h = 8 yard
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 8 = 226.29 cubic yard
2. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 2inches, h = 11
= [tex]\frac{1}{3}[/tex] x [tex]2^{2}[/tex] x [tex]\frac{22}{7}[/tex] x 11 = 46.1 cubic inches
3. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 8, h = 12
= [tex]\frac{22}{7}[/tex] x [tex]8^{2}[/tex] x 12 = 2413.71 cubic inches
4. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 4, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]4^{2}[/tex] x 14 = 234.67 cubic millimeter
5. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 5, h = 13
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 13 = 340.48 cubic yards
6. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 3, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 4 = 113.14 cubic feet
7. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. r = 6, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 14 = 528 cubic centimeter
8. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 6, h = 8
= [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 8 = 905.14 cubic centimeter
9. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 1.5, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]1.5^{2}[/tex] x 4 = 56.57 cubic feet
In conclusion, the volume of cylinders and cones for the given dimensions are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
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Help please thank you
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other. The supplementary angles are 153° and 27°. The Complementary angles are 34° and 56°.
What are Supplementary Angles?When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
What are Complementary Angles?When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
The supplementary angles are 153° and 27°.
The Complementary angles are 34° and 56°.
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PLEASE HELP I WILL GIVE BRAINLIEST!!
Find an angle in the range between 0 and 2ㅠ radians that is coterminal with
-ㅠ/2
a) 7ㅠ/2
b) 3ㅠ/2
C) 5ㅠ/2
d) ㅠ/2
The coterminal angle to -ㅠ/2 in the range between 0 and 2ㅠ radians is 3ㅠ/2.
How to find a coterminal angle?
For any angle A, all the coterminal angles are of the form:
B = A + n*(2ㅠ).
Where n is an integer different than zero.
In this case, the angle is A = -ㅠ/2
So the coterminal angles are of the form:
B = -ㅠ/2 + n*(2ㅠ)
We want it to be between 0 and 2ㅠ, so we can define n = 1, then we get:
B = -ㅠ/2 + (2ㅠ) = -ㅠ/2 + ((4/2)ㅠ) = 3ㅠ/2
Then we can conclude that the correct option is b.
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pleaseeee help I really need help so baddd
Answer:
Step-by-step explanation:
What does the remainder theorem conclude given that f(x)x+3 has a remainder of 11?
By the remainder theorem of polynomial division, the complete equation is f(-3) = 11
How to complete the blanks?The equation is given as:
f(x)/x + 3
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Given that the quotient has a remainder of 11.
It means that:
f(-3) = 11
Hence, the complete equation is f(-3) = 11
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Protons have a small negative electrical charge.
True
False
Answer:
False
Step-by-step explanation:
Protons have positive charge.
Answer:
Protons have a positive charge.
Step-by-step explanation: