In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6 others.
Proportionate Stratified Sample
A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.
Calculating the Proportionate Stratified Sample
The given percentage of -
Whites = 60%
Latinos = 20%
Blacks = 5%
Strength of the sample = 120
⇒ Number of Whites = 60% of 120
= 0.6 × 120
=72
Number of Latinos = 20% of 120
= 0.2 × 120
=24
Proportionate Stratified Sample of Blacks and Others
Count of Blacks = 15 % of 120
= 0.15 × 120
= 18
Count of others = 5% of 120
= 0.05 × 120
6
Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.
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Condense to a single logarithm : log 12 18+3 log 12 2
Answer:
2 or [tex] \log_{12} 144 [/tex]
Step-by-step explanation:
I assume 12 is the base.
[tex] \log_{12} 18 + 3 \log_{12} 2 = [/tex]
[tex] = \log_{12} 18 + \log_{12} 2^3 [/tex]
[tex] = \log_{12} (18 \times 8) [/tex]
[tex] = \log_{12} 144 [/tex]
[tex] = \log_{12} 12^2 [/tex]
[tex] = 2\log_{12} 12 [/tex]
[tex] = 2 [/tex]
The entire expression simplifies to 2, but if you need the simplest log expression, then you can use
[tex] \log_{12} 144 [/tex]
1/6(x + 6) = 11 What is x
Answer:
x = 60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
[tex]\frac{1}{6}[/tex](x+6)=11
[tex]\frac{1}{6}[/tex]x + 1 = 11
[tex]\frac{1}{6}[/tex]x +1 -1 = 11 -1
[tex]\frac{1}{6}[/tex]x * 6 = 10 *6
x = 60
To double check
[tex]\frac{1}{6}[/tex](60+6)=11
10+1 = 11
11 = 11
if f(x)=3x-4 and g(x)=x^2 -1
what is f(g(-3))?
a) -34
b) 8
c) 20
d) 168
Write the equation of the line that passes through the points (8, 14) and (-2,-16) in slope-intercept form.
Answer:
y = 3x - 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 14) and (x₂, y₂ ) = (- 2, - 16)
m = [tex]\frac{-16-14}{-2-8}[/tex] = [tex]\frac{-30}{-10}[/tex] = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 14 ) , then
14 = 24 + c ⇒ c = 14 - 24 = - 10
y = 3x - 10 ← equation of line
1 + 7x
The sum of two numbersis 23. The greater number
is b. Select the expression that represents the lesser
number.
Answer:
Step-by-step explanation:
a+b = 23
a<b
a = 23-b
A
walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the equation that represents the new path.
Answer:
We are given the path, y=-3x-6
The general form of the straight line is 'y=mx+b', where 'm' is the slope and 'b' is the y-intercept.
Thus, the slope of the given line is -3.
As, we have that the incipient path is perpendicular to the given path.
And, we ken that, 'Product of slopes of perpendicular lines is -1'.
Since, the incipient path passes through the point (-3,3). Superseding the values in the general form, we get,
b= 3+1
b= 4.
Step-by-step explanation:
If the sales tax rate is 7.5% in New York State, then how much sales tax would you pay in Albany for a $34 pair of pants? What is the final cost?
Answer:
Sales Tax $2.55
Final Cost $36.55
Step-by-step explanation:
Finding sales tax
34 * 7.5%= 2.55
Multiply the tax with the original cost, that will be your sales tax
Finding final cost
34 + 2.55= 36.55
Add your sales tax with the original cost, now you have the final total
Your parents are building a pool that is 7 ft wide and 12 ft long. They want to put a walkway around the pool that is x ft wide on all sides. Write a polynomial that represents the combined area of the pool and walkway. Answer needs to be in standard form and use x as your variable.
Answer:
Combined area = 4[tex]x^{2}[/tex] + 38x + 84
Step-by-step explanation:
The rectangle formed by the pool and walkway is 12 + 2x long and 7 + 2x wide.
Area of the rectangle = lw = (2x + 12)(2x + 7) = 4[tex]x^{2}[/tex] + 38x + 84
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First okay and second umm my what?! Lol
The answer is : - 112
We add 14 to both side
-16x - 14 = -126
+ 14 +14
-16x = - 112. <- that’s the answer
Then we divide both sides by 16
X = 7
Ta -Da!!
Also I’ll leave this.....
Solve for xxx.
Your answer must be simplified.
15 < -5 x
Answer:
x < - 3
Step-by-step explanation:
Given
15 < - 5x
Divide both sides by - 5, reversing the symbol as a result of dividing by a negative quantity
- 3 > x , that is
x < - 3
The simplified expression is x < -3.
What is an inequality?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is the condition of being unequal. It is used most often to compare two numbers on the number line by their size.
For the given situation,
The expression is 15 < -5x
⇒ [tex]15 < -5 x[/tex]
Divide both sides by -5,
⇒ [tex]\frac{15}{-5} < \frac{-5}{-5} x[/tex]
When we divide an inequality with negative number, we need to change the sign,
⇒ [tex]-3 > x[/tex]
⇒ [tex]x < -3[/tex]
Hence we can conclude that the simplified expression is x < -3.
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Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer
Describe how you would estimate the square root of a number that is not a perfect square without using a calculator
Answer:
The square root must be between the square roots of the perfect squares just above and just below your number.
For example the square root of 89 must be between 9 and 10.
Step-by-step explanation:
el área de un mosaico es de 900cm2 ¿cuánto mide por lado cada mosaico
Answer:
El lado de cada mosaico tiene una longitud de 30 cm.
Step-by-step explanation:
El area de un mosaico cuadrado es:
[tex]A=l^{2}[/tex]
Donde l es el lado del mosaico.
Entonces, si sabes que el area es 900 cm², el lado valdra:
[tex]900=l^{2}[/tex]
[tex]l=\sqrt{900}[/tex]
[tex]l=30\: cm[/tex]
Por lo tanto el lado de cada mosaico tiene una longitud de 30 cm.
Espero te haya servido!
Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now attempt two free throws. The probability that Helen makes the second free throw given that she made the first is 0.85. What is the probability that she makes both free throws?
Answer: 0.6375
Step-by-step explanation:
Let's assume that the event that she'll make the first shot is given as P(A) while making the second shot is P(B). Therefore, P(A/B) = 0.85
Therefore, the probability that she makes both free throws will be denoted as:
= 0.75 × 0.85
= 0.6375
Pleaseeee help I need a answer fast
Answer:
300
Step-by-step explanation:
im smart
Write the equation 9 = -5x + 4 in the form ax + b = c, where c = 9.
What are the values of a and b?
Answer:
a = - 5x and b= 4
Step-by-step explanation:
So it becomes - 5x +4=9
Hope this helps pls tell if any mistakes
Answer:
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PLEASE ANSWER!!!!!
An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth.
[tex] \sin = \frac{opp}{hyp} [/tex]
[tex] \sin(15) = \frac{280}{hyp} [/tex]
[tex]hyp = \frac{280}{ \sin(15) } [/tex]
[tex]hyp = 1081.836925 \: feet[/tex]
The direct line distance from the eagle to the mouse is 1081.837 feet
find the value of a and b of a+root5 is (root5+root3)(root5-root3)
Given:
Consider the value of [tex]a+b\sqrt{5}[/tex] is [tex](\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex].
To find:
The values of a and b.
Solution:
According to the given information,
[tex]a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})[/tex]
[tex]a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]a+b\sqrt{5}=5-3[/tex]
[tex]a+b\sqrt{5}=2[/tex]
It can be written as
[tex]a+b\sqrt{5}=2+0\sqrt{5}[/tex]
On comparing both sides, we get
[tex]a=2,b=0[/tex]
Therefore, the value of a is 2 and the value of b is equal to 0.
Please answer ASAP
The perimeter of a rectangle is 176 m. The length is equal to 3 times the width decreased by 4. Find the dimensions of the rectangle.
Answer:
L=65m
W=23m
Step-by-step explanation:
[tex]3W-4=L\\2L+2W=176\\\\2L+2W=176\\-2L+6W=8\\8W=184\\W=23m\\L=23*3-4=65m[/tex]
The length and width of the rectangle are 63m and 25m.
What is a rectangle?A rectangle is a quadrilateral, a 2d shape that has four sides and four vertices.
We have,
The perimeter of a rectangle = 176 m
Length of the rectangle = L = 3 x (W- 4 )
Width of the rectangle = W
The perimeter of a rectangle is given by:
176 = 2 ( L + W )
176 = 2 ( 3 ( W - 4 ) + W )
176 = 2 ( 3W - 12 + W )
176 = 2 ( 4W - 12 )
176 = 8W - 24
176 + 24 = 8W
200 = 8W
W = 200 / 8
W = 25 m
Now,
Put W = 25 in L = 3 x ( W - 4 )
L = 3 x ( 25 - 4 )
L = 3 x 21
L = 63 m
We can cross-check:
Perimeter = 2 ( 63 + 25 ) = 2 ( 88 ) = 176 m
Thus the length and width of the rectangle are 63m and 25m.
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anyone think they could help me with this question???
Answer:
61
Step-by-step explanation:
As we can see the triangles are congruent so
< F = < C ( being corresponding angles of congruent triangle)
< C = 29
Now
<A +<B + <C = 180° { being sum of angles of triangle }
5x + 1 + 90 + 29 = 180°
5x = 180° - 120°
5x = 60°
x = 12°
<A = 5 * 12° + 1 = 61°
Hope it will help :)
The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of CD player with a selling price of $110
Answer:
Total Cost = 1.05x
CD Player cost = 110*1.05 = $115.50
Step-by-step explanation:
is 8 x 2/8 less than 8 or greater than 8
Answer: yes if is
Step-by-step explanation:
What is the area of cross-section ADGF of this right rectangular prism?
A.
20 square units
B.
48 square units
C.
52 square units
D.
65 square units
Answer:
C.52 square units
Step-by-step explanation:
We are given that
Length of cross-section ADGF,l=13units
Length of cross-section ADGF, b=4 units
We have to find the area of cross-section ADGF of this right rectangular prism.
We know that
Area of rectangle=[tex]l\times b[/tex]
Using the formula
Area of cross-section ADGF of this right rectangular prism
=[tex]13\times 4[/tex]
Area of cross-section ADGF of this right rectangular prism=52square units
Option C is correct.
C.52 square units
Answer:
i hope this helps
Step-by-step explanation:
please help me I will mark brainiest
Answer:
x = 6
Step-by-step explanation:
To solve for x, do inverse operations on both sides of the equation:
x + 4 = 10
- 4 - 4
---------------
x = 6
x = 6
Answer:
6
Step-by-step explanation:
x + 4 = 10
6 + 4 = 10
factor out the gcf 12y³+10y²
Answer:
Find the prime factors of each term in order to find the greatest common factor (GCF).
2y^2
Factoring out the greatest common factor (GCF)To factor the GCF out of a polynomial, we do the following: Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
Step-by-step explanation:
Hope it is helpful.....
someone who can actually give the answer please answer this please! do not put nothing crazy or get reported!!
Find the zeros of this polynomial.
Answer:you’ll find the answer just by understanding and looking at the photo
Step-by-step explanation:
Answer the photo below thanks
the cost of contructing a 63mcube wall is rs 84000. find the volume of each brick if the cost of a bric is rs 13
Answer:
0.00975 m^3 each
Step-by-step explanation:
rs 84000 / rs 13 = 6461.539 bricks
63 m^3 / 6461.539 = 0.00975 m^3 each
What is the exact length of each side?
Answer:
[tex]6a^{2} \sqrt{ab}[/tex]
Step-by-step explanation:
area of square = side x side
thus, each side = square root of area
[tex]\sqrt{36a^5b}[/tex] = 6[tex]\sqrt{a^{4} ab}[/tex] = 6[tex]a^{2}[/tex][tex]\sqrt{ab}[/tex]
Identify the cross section that results from slicing the three-dimensional figure with a plane that is parallel to its base
A)Pyramid
B)Rectangle
C)Square
D)Triangle
Answer:
D) triangle
Step-by-step answer:
A pyramid is a three-dimensional figure with a plane that is parallel to its base.
PyramidA three dimensional figure is a figure with a length, width and height. 3D shapes have faces, edges, and vertices.
Rectangle, square and triangle are two dimensional shapes while pyramid is a three dimensional shape.
A pyramid is a three-dimensional figure with a plane that is parallel to its base.
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Help please! Thank youuuuuy
Step-by-step explanation:
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