Answer:
81.25 ; 3091.48 ; 55.60
Step-by-step explanation:
Given the data :
45, 60, 25, 55, 75, 90, 100, 120, 105, 80, 0, 220
The mean :
ΣX/n ; n = sample size
ΣX = 45+60+25+55+75+90+100+120+105+80+0+220 = 975
n = 12
Mean = 975 / 12 = 81.25
The variance :
Σ(X - m)^2 / n - 1
Using calculator to save computation time :
The variance : (34006.24997 / 11)
Variance = 3091.48
The standard deviation :
Sqrt(Variance) = sqrt(3091.48) = 55.60
A model giving the area A, in square meters, of a path is A = x^2 - 18x +80. Which equivalent expression shows the length and the width of the path?
A. A= (x-15)(x-3)
B. A = (x-10)(x-8)
C. A= (x-16)(x-5)
D. A = (x-20)(x-4)
Answer:
B
Step-by-step explanation:
The equivalent expression shows the length and the width of the path is (x-10)(x-8).
What is Quadratic Equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a≠ 0) for an equation to be a quadratic equation. The x²term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are typically expressed as integral values rather than fractions or decimals.
Given:
A = x² - 18x +80.
Now, factorizing
x² - 10x - 8x + 80
=x(x-10) - 8(x-10)
=(x-8)(x-10)
Hence, equivalent expression shows the length and the width of the path is (x-10)(x-8).
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There are 9 times as many cubes in the black bag as in the green bag. The green bag has 12 cubes. How many cubes are in the black bag?
Answer:
108
Step-by-step explanation:
Answer:
108 cubes
Step-by-step explanation:
9 times 12 equals 108
9 • 12 = 108 cubes
HELP ASAP WILL GIVE 25 POINTS
Write an equation of a line that is parallel to y = x - 7 and passes through the point (-6, -11).
Answer:
y = x - 5
Step-by-step explanation:
Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.
In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:
-11 = -6 + b
Then b must be -5, and so the desired new equation is
y = x - 5
Based on a sample of 100 employees a 95% confidence interval is calculated for the mean age of all employees at a large firm. The interval is (34.5 years, 47.2 years).
A. What was the sample mean?
B. Find the margin of error?
C. Find the critical value tc for:
a. a 90% confidence level when the sample size is 22.
b. an 80% confidence level when the sample size is 49.
Answer:
a
[tex]\= x = 40.85[/tex]
b
[tex]E = 5.85[/tex]
Ca
[tex]t_c = 2.08 [/tex]
Cb
[tex] t_c = 1.282 [/tex]
Explanation:
From the question we are told that
The sample size is n = 100
The upper limit of the 95% confidence interval is b = 47.2 years
The lower limit of the 95% confidence interval is a = 34.5 years
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{a + b }{2}[/tex]
=> [tex]\= x = \frac{47.2 + 34.5 }{2}[/tex]
=> [tex]\= x = 40.85[/tex]
Generally the margin of error is mathematically represented as
[tex]E = \frac{b- a }{ 2}[/tex]
=> [tex]E = \frac{47.2- 34.5 }{ 2}[/tex]
=> [tex]E = 5.85[/tex]
Considering question C a
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
The sample size is n = 22
Given that the sample size is not sufficient enough i.e [tex]n < 30[/tex] we will make use of the student t distribution table
Generally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 22 - 1[/tex]
=> [tex]df = 21[/tex]
Generally from the student t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of 21 is
[tex]t_c =t_{\frac{\alpha }{2} , 21 } = 2.08 [/tex]
Considering question C b
From the question we are told the confidence level is 80% , hence the level of significance is
[tex]\alpha = (100 - 80 ) \%[/tex]
=> [tex]\alpha = 0.20[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex] t_c =Z_{\frac{\alpha }{2} } = 1.282 [/tex]
What is the solution to this equation 2x + 10 equals 28
Answer:
X=9
Step-by-step explanation:
2X+10=28
-10 -10
2X=28
DIVIDE BOTH SIDES BY 2
In the image...i showed the work
Rick is taking a 1-mile ride on his bicycle. For each rotation of his tire, he travels 72 inches. How many rotations will his tire make during the 1-mile trip?
O 73 rotations
O 83 rotations
O 780 rotations
O 880 rotations
SHOW YOUR WORK!!!
Answer:
880 rotations or D
Step-by-step explanation:
72 inches = 72 / 12 = 6 feet
1 mile = 5280 feet
1 rotation covers 6 feet
x rotations covers 5280 feet
1/x = 6/5280 Cross multiply
6x = 5280 * 1 Divide by 6
x = 5280 /6
x = 880
D
What is the quotient of Three-fifths and StartFraction 1 Over 10 EndFraction?
A number line going from 0 to 1 in increments of 0.2.
One-sixth
One-third
3
6
Answer:
D:6
Step-by-step explanation:
3/5 = 6/10
6/10 divided by 1/10 equals 6
so 6 is your answer.
Answer:
d
Step-by-step explanation:
Solve for x
4x + 188
6x+216
(2/3)x = 12
what does x =
Answer:
x=18
Step-by-step explanation:
To solve for x you need to times both sides by 3/2 so then 12*3/2=12*1.5=18.
(can I get brainliest please)
Answer:
X = 18
Step-by-step explanation:
(2/3)X = 12
X = 12/(2/3)
X = 36/2
X = 18
What is the range in interval notation?
Answer:
The blue box
Step-by-step explanation:
Youre talking about range which takes place on the y-axis (domain is the x-axis).
The top point is an open circle which indicates in the math world the parentheses and the bottom point 1 in a bracket as its a closed circle.
Two shirt screening companies charge a set up fee and a charge for
each shirt made. The table shows the total costs for the company
Shirt Express. The total cost y (in dollars) for x shirts made by Shirt
Custom is represented by the equation y = 8 + 46.
Answer:
y=54
Step-by-step explanation:
y = 2(x - 2)2 + 1
10
What is the
a. Vertex
b. Axls of Symmetry line: x =
c.y.Intercepts:(
Answer:
Step-by-step explanation:
Vertex
Estimate the solution of 4x + 5 = 34.
Answer:
29/4
Step-by-step explanation:
4x=29
x=29/4
The value of x and the solution of the equation is 7.25.
What is an Equation?An equation is a statement that is formed when two algebraic expressions are equated by an equal sign.
The solution of 4x+5 = 34 is
4x = 34-5
4x = 29
x = 29/4
x = 7.25
The value of x and the solution of the equation is 7.25.
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n ÷ -6 = 4 - (-2)
-12
36
-36
12 ********************************
Answer:12
Step-by-step explanation:
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The price of a television was increased from $200 to $250. By what percentage was the price of the television increased
Answer:
20%
Step-by-step explanation:
cuz quick meths
Joey wants to paint this side of his cottage. What is the area of this side?
A. 56 square feet
B. 238 square feet
C. 294 square feet
D. 462 square feet
Answer:
238 B
Step-by-step explanation:
8.5*28
HELP ME PLEASE!!!
On a scale drawing of a house, the dimensions of the living room are 4 inches by 3 inches. If the scale drawing is 1 in: 6 ft , find the actual length and width of the living room.
Answer:
The width is 18
Step-by-step explanation:
6x3 and get 18 as the width
Each cube is 1.5 cm long. Calculate the surface area.
Answer:
13.5cm square
Step-by-step explanation:
A=l×w = 1.5×1.5=2.25cm square
SA=2.25×6=13.5cm square
The surface area of the cube is 49.5 cm². Thus, option C is correct.
What is cube?A cube is a three-dimensional solid object having six square faces, facets, or sides, three of which meet at each vertex. It is a hexagon when viewed from a corner, and its net is commonly portrayed as a cross. The cube is one of the five Platonic solids and the only regular hexahedron.
The surface area of a solid item is a measurement of the entire area occupied by the object's surface.
The surface area formula is six times the square of the length of the cube's sides. It is represented as 6a2, where is the cube's side length. It is, in essence, the whole surface area.
Area of Cube = side*side
= 1.5x1.5
=2.25cm²
A total of 22 surfaces are exposed. So, the surface area of the cube is,
=22* 2.25
= 49.5 cm²
Therefore, option C is correct.
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Complete question is mentioned in the image below.
Find the location of A' given that A is (7, 1).
Translate 1 unit left.
The location of A' is ____
Answer:
We conclude that the location of A' is: A'(6, 1)
Step-by-step explanation:
Given
A(7, 1)To determine:
The location of A'
Translation Rule:
As we have to translate 1 unit left, meaning we need to subtract 1 unit from the x-coordinate of point A(7, 1) to determine the location of A'.
In other words, the translation rule is:
A(x, y) → A'(x-1, y)
as
A(7, 1)
so
A(7, 1) → A'(7-1, 1) = A'(6, 1)
Therefore, we conclude that the location of A' is: A'(6, 1)
HELPP WITHH MATHHH PLEASE SMART PEOPLE
Answer:
is not; 4t
Step-by-step explanation:
Because when you switch the signs for substraction like 2-3 you will get -1, but if you do 3-2, then youll get 1. The Same goes for this question. If you plug in 2 for t, like 13(2)-4(2), it will be 26-8, which is 18. But if you do the same for the other equation, 4(2)-13(2), you will get 8-26, which equals -18. So -18 does not equal 18 because one postive and the other is negative.
Answer:
is not; -4t
Step-by-step explanation:
It's not the same because the negative sign always belongs to the number in front of it.
What is the value of t in this situation 2t+5=2t+5
Answer:
t = infinite amount of solutions
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
2t + 5 = 2t + 5
Step 2: Solve for t
Subtract 5 on both sides: 2t = 2tDivide 2 on both sides: t = tHere we see that t does indeed equal t.
∴ t = infinite amount of solutions
Please give me the correct answer
in a packet or Skittles there are, 40 Skittles,30 are red how many Skittles are not red
Answer:
10
Step-by-step explanation:
hope this helps ")
Which polynomial represents the product of 2x - 4 and x2 + 6x - 2 ?
ОА
2x3 + 8
thing
B
2x3 + 8x2 - 4x + 8
с
2x3 + 8x2 - 28x + 8
D
2x3 - 24x - 2
Answer:
C. [tex] 2x^3 + 8x^2 - 28x + 8 [/tex]
Step-by-step explanation:
Product of [tex] 2x - 4 [/tex] and [tex] x^2 + 6x - 2 [/tex]
[tex] (2x - 4)(x^2 + 6x - 2) [/tex]
[tex] 2x(x^2 + 6x - 2) -4(x^2 + 6x - 2) [/tex] (distributive property)
[tex] 2x^3 + 12x^2 - 4x -4x^2 - 24x + 8 [/tex]
Collect like terms
[tex] 2x^3 + 12x^2 - 4x^2 - 4x - 24x + 8 [/tex]
[tex] 2x^3 + 8x^2 - 28x + 8 [/tex]
ANSWER ASAP PLEASE
If Jose drove 330 miles in 5.5 hours, how many miles did he drive per hour?
Answer:
60mph
Step-by-step explanation:
330 divided by 5.5 is 60
is 42x - 56y equivalent to 42 (x + 14y)
Answer:
No
Step-by-step explanation:
42x+588
What is 0.612 repeating (meaning the repeating line is over 612) as a fraction
Answer:
[tex]\frac{612}{999}[/tex]
Step-by-step explanation:
To convert repeating decimals to fractions, you take the numbers that are repeating, in this case 612, and you see how many numbers are repeating. Here we have 3 numbers repeating and so you would divide 612 by 3 9's meaning 999. So 0.612 repeating is equal to [tex]\frac{612}{999}[/tex]. To make sure the answer is right, you can divide the numbers in a calculator to make sure you get the correct decimal.
Select two ratios that are equivalent to 2:9
Choose 2 correct answers 40 points
Answer:
4:18 6:27 8:36
Step-by-step explanation:
I NEED HELP PLZ ITS FOR MY FINAL
