Answer:
a= -3
Step-by-step explanation:
first distrubute the parenthesis -2(a-3)
-2a+ 6= 12
then move the like terms
6 becomes -6 and subtract to both sides so 6-6 cancels out and you are left with 12-6 which gives you 6
then you have -2a = 6
lastly divide on both sides and you get
-2a÷ -2 (cancels out)
6÷ -2
and the answer is
a= -3
Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of adults showed indicating that their financial security was more than fair. In February of 2010, a sample of adults showed indicating that their financial security was more than fair. a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.\
Complete Question
Country financials, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more that fair. In Feb 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair.
a
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b
What is the sample proportion indicating that their financial security was more that fair in 2012?In 2010?
c
Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?
Answer:
a
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 \ne p_2[/tex]
b
in 2012 [tex]\r p_1 =0.41[/tex]
in 2010 [tex]\r p_2 =0.35[/tex]
c
The p-value is [tex]p-value = 0.0072 [/tex]
The conclusion is
There is sufficient evidence to conclude that the proportion of those indicating that financial security is more fair in Feb 2010 is different from the proportion of those indicating that financial security is more fair in Feb 2012.
Step-by-step explanation:
From the question we are told that
The sample size in 2012 is [tex]n_1 = 1000[/tex]
The number that indicated that their finance was more than fail is k = 410
The sample size in 2010 is [tex]n_2 = 900[/tex]
The number that indicated that their finance was more than fail is u = 315
The level of significance is [tex] \alpha = 0.05[/ex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 \ne p_2[/tex]
Generally the sample proportion for 2012 is mathematically represented as
[tex]\r p_1 = \frac{k}{n_1}[/tex]
=> [tex]\r p_1 = \frac{410}{1000}[/tex]
=> [tex]\r p_1 =0.41[/tex]
Generally the sample proportion for 2010 is mathematically represented as
[tex]\r p_2 = \frac{u}{n_2}[/tex]
=> [tex]\r p_2 = \frac{315}{900}[/tex]
=> [tex]\r p_2 =0.35[/tex]
Generally the pooled sample proportion is mathematically represented as
[tex]\r p = \frac{k + u }{n_1 + n_2}[/tex]
=> [tex]\r p = \frac{410 + 315 }{1000+ 900}[/tex]
=> [tex]\r p = 0.3816 [/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{( \r p_1 - \r p_2 ) - 0}{\sqrt{\r p (1 - \r p ) ( \frac{1}{n_1} +\frac{1}{n_2} )} }[/tex]
[tex]z = \frac{( 0.41 -0.35 ) - 0}{\sqrt{0.3816 (1 - 0.3816 ) ( \frac{1}{1000} +\frac{1}{900} )} }[/tex]
[tex]z = \frac{( 0.41 -0.35 ) - 0}{\sqrt{0.3816 (1 - 0.3816 ) ( \frac{1}{1000} +\frac{1}{900} )} }[/tex]
[tex]z = 2.688[/tex]
Generally the p- value is mathematically represented as
[tex]p-value = 2 P(Z >2.688 )[/tex]
From the z -table
[tex]P(Z > 2.688) = 0.0036 [/tex]
So
[tex]p-value = 2 *0.0036 [/tex]
[tex]p-value = 0.0072 [/tex]
So from the p-value obtained we see that p-value < [tex]\alpha[/tex] so we reject the null hypothesis
Thus there is sufficient evidence to conclude that the proportion of financial security is more fair in Feb 2010 is different from the proportion of financial security is more fair in Feb 2012.
John ran 3 miles in 25.2 minutes. The equation y = 8.5x, where x represents the number of miles and y represents the total time in minutes, represents this situation. What is the constant of proportionality? What does the constant of proportionality represent in the context of the problem?
Step-by-step explanation:
It is given that,
John ran 3 miles in 25.2 minutes. We can find the speed of john as follows :
Speed = distance/time
v = [tex]\dfrac{3\ \text{miles}}{25.2\ \text{minutes}}=0.1190\ \text{miles/minutes}[/tex]
The equation y = 8.5x, where x represents the number of miles and y represents the total time in minutes, represents this situation. y is proportional to x with constant of proportionality 8.5.
Velocity of John is 0.1190 miles/minute. We can write it in the form of equation as :
y = 0.1190x
In this problem, the constant of proportionality is 0.1190.
Which equation is true when X = -5?
2/5x+15-17
7+5x = 18
6- 4x = -14
0.5-2.4x = 12.5
Answer: 0.5-2.4x=12.5
Step-by-step explanation:
-2.4(-5)=12
0.5+12=12.5
if the first one was blurry but pls help
Answer:
400 minutes it will take
Steve stayed after school for extra activities 55% of the 180 school days this year. How many days did Steve stay after school?
Answer:
11/20 or 99/180 days
Step-by-step explanation:
55/100 converted to ?/180
180/100=1.8
so you would do the same on the numerator which is 55*1.8=99
99/180= 33/60=11/20
Answer:
125
Step-by-step explanation:
What times 21 equals 7? Is that even possible to multiply something by 21 to get 7?
Answer:
Step-by-step explanation:
FIRST ANSWER GETS CROWNED BRAINLIEST!!!
If the slope of a line is 1/2, find x when (-4, 12) and (x, 5) ?
Please show formula.
Answer:
x = -18
Step-by-step explanation:
Well you just have to do the this formula to find the slope
[tex]\frac{y2 - y1}{x2 - x1}[/tex] Plug in
[tex]\frac{5 - 12}{x - -4 }[/tex] = [tex]\frac{-7}{?}[/tex]=[tex]\frac{1}{2}[/tex]
So we know x will have to be a negative to get 1/2
I would think x = -18 because -18 - -4 = -14 so it would look like this
[tex]\frac{5 - 12}{-18 - -4}[/tex] = [tex]\frac{-7}{-14}[/tex] =[tex]\frac{1}{2}[/tex]
When you further simplify -7/-14 you get 1/2
There are 12 girls for every 16 boy in class.
What is the ratio of boys to girls?
Write the ratio 3 ways.
if f(x)=3^x+10 and g(x)=2x-4, find (f-g)(x)
=====================================
Work Shown:
(f - g)(x) = f(x) - g(x)
(f - g)(x) = ( f(x) ) - ( g(x) )
(f - g)(x) = ( 3^x + 10 ) - ( 2x-4 )
(f - g)(x) = 3^x + 10 - 2x+4
(f - g)(x) = 3^x - 2x + (10+4)
(f - g)(x) = 3^x - 2x + 14
Wade has three more quarters than dimes. The total value of the dimes and quarters together is $13. How many quarters does he have?
Answer:
38 Quarters
Step-by-step explanation:
D=number of dimes; Q=number of quarters=D+3
.
$0.10D+$0.25Q=$13
$0.10D+$0.25(D+3)=$13
$0.10D+$0.25D+$0.75=$13
$0.35D=$12.25
D=35
.
Q=D+3=35+3=38
ANSWER: He has 38 quarters.
Please help will mark brainliest and 20 points
Answer:
10 weeks
Step-by-step explanation:
she already has 14
so 5 x 10 = 50
14+50=64
Line v passes through point (6, 6) and is perpendicular to the graph of y = 34x – 11. Line w is parallel to line v and passes through point (–6, 10). Which is the equation of line w in slope-intercept form?
A. y = 34x + 2
B. y = –34x + 2
C. y = 43x + 2
D. y = –43x + 2
I need to figure this out
Answer:
plug in the missing numbers and you have the answers
Step-by-step explanation:
6×5=232+4×3=4427×3-(16+3×5)=507×5÷3+2=13.62×7-4×3=2Which statements are true about the graph of the function f(x) = x2 - 8x + 5? Select three options.
The function in vertex form is f(x) = (x - 4)2 - 11.
The vertex of the function is (-8,5).
The axis of symmetry is x = 5.
The y-intercept of the function is (0.5).
The function crosses the x-axis twice
Answer:
A, D, E
Step-by-step explanation:
The statements that are true about the graph of the function are
The function in vertex form is f(x) = (x - 4)^2 - 11.The y-intercept of the function is (0,5).The function crosses the x-axis twiceVertex and intercept of a functionThe standard equation of a function in vertex form is expreseed as:
a(x-h)^2 + k
Given the quadaratic function f(x) = x^2 - 8x + 5, the expression in vertex form is given as:
f(x) = (x^2-8x + 4^2) - 16 + 5
f(x) = (x-4)^2 - 16 + 5
f(x) = (x-4)^2 - 11
Find the y-intercept.
This is the point here x = 0
f(0) = 0^2 - 8(0) + 5
f(0) = 5
Hence the y-intercept of the function is at (0, 5)
Since the quadratic function has a leading degree of 2, hence the function crosses the x-axis twice
Learn more on vertex and intercepts here: https://brainly.com/question/12778829
What is the measure of the missing angle?
76
166
86
156
0.04 Equation Editor
Answer:
Step-by-step explanation:
Equation 3.0.
2x-4y=28 solve for y
Answer:
y=7+1/2x
Step-by-step explanation:
Hope this helps
tell me how to solve 3 1/2 x 2 3/4
Answer:
9.625
Step-by-step explanation:
(3 1/2) x (2 3/4) = 9.625
Answer:
.........................
A person places $290 in an investment account earning an annual rate of 2.2%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.
Answer:
$430.90Step-by-step explanation:
Given that the principal p= $290
rate r= 2.2% 2.2/100 =0.022
time t= 18years
by applying the expression
[tex]V = Pe^{rt}[/tex]
We have
[tex]V = 290e^{0.022*18}\\\\V=290e^{0.396}\\\\V=290*1.48586931755\\\\V=$430.90[/tex]
Hence after 18years the money in the account will be $430.90
How many solutions does this equation have ?
2(2x-1)=(x+1)+3(x-1)
Which equation shows a proportional relationship? *
y= -2x +5
y= 3+ 5x
y= -3x
Answer:
y= -3x
Step-by-step explanation:
The graph of a line with a proportional relationship would have the line go through the origin.
Since the 'y=-3x' equation only shows the slope of the line, it goes through (0,0), or the origin, as it's y-intercept.
y= -3x should be the correct answer.
Hope this helps.
Let p: A student plays basketball.
Let q: A student plays tennis.
How many students play both basketball and tennis?
4
8
32
36
Answer:
the answer is 4
Step-by-step explanation:
By the concept of the intersection of sets 4 students play both basketball and tennis
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
In this example, we search for the group of students who participate in both sports because we are aware that p is the set formed by the students who play basketball and q is the group formed by the students who play tennis. In other words, we seek the point at where the sets p and q intersect.
Each set is represented by a circle in the Venn diagram, and the set produced by the intersection of p and q is represented by the area where the two circles overlap.
This graph demonstrates that there are 4 kids that participate in both basketball and tennis.
learn more about sets and Venn diagrams here :
https://brainly.com/question/28318748
#SPJ7
2. Which property is being used in the second line?
line 1: (4.5.-1). -6
line 2: 4.5 .(-1.-6)
line 3: 4.5 .6
line 4: 27
O A. Distributive
O B. Commutative
O C. Associative
O D. Additive Inverse
Answer:
C associative to associate both of them
Which function h(x) results when g(x) is translated IT
units right and 1 unit down?
Answer:
b on edge
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Got it right on Edge
PLSS help i dont understand I found w =59 but dont know how to find the rest
Answer:
i think that Y= 59 because of it being a vertically opposite angle and X= 121 because of the line being a straight one and angles on a straight line add to 180
Step-by-step explanation:
hope this helps :))
Find the missing number?
Answer:
$4.60 and $18.40
Step-by-step explanation:
The total cost of one milk carton is $2.30. I got this by dividing $9.20 by 4. If you multiply $2.30 by 2, you get $4.60. If you multiply $2.30 by 8, you'll get $18.40.
Step by step 2 step equation: v/6-4=-5
What is the area of this triangle? And it's not 60, I already checked. PLEASE EXPLAIN!!!!
Answer:
A = 4 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 b*h
The base is 4 and the height is 2
A = 1/2 ( 4*2)
A = 1/2*8
A = 4 cm^2
Answer:
4
Step-by-step explanation:
A = BH/2
or Area = Base multiplied by Hieght divided by 2.
(b)4 x (h)2 = 8
8/2 = 4
During a science experiment, your teacher does a demonstration. She takes a
small piece of rope, weighs it to find its starting weight, burns it, and then
weighs it again. The final mass of the product is different from the starting
weight of the reactant.
Why is the final mass different? Does this mean that the product has less
mass? Why or why not?
Answer:
less mass
Step-by-step explanation:
The product has less mass because some of its mass got burned. Hope this helps!
some parts of the rope turned into gasses because of the intense heat (fire)
what's the slope of these two lines
Answer:
the green line is 3/4 and the blue line is-3/4