The test is to find out if there is a difference in the proportion of the number of autism in two samples differentiated by the use of vitamins.
The test statistic for the test is approximately 2.98
The p-value associated is 0.0028
Reasons:
The given parameters are;
[tex]\begin{array}{|l|c|c|c|}&\mathbf{\underline{Autism}}&\mathbf{\underline{Typical \ Development }}&\mathbf{\underline{Total}}\\No \ vitamin&111&70&181\\Vitamin&143&159&302\\Total&254&229&483\end{array}\right][/tex]
The null hypothesis is H₀; [tex]\hat{p}_1 = \hat{p}_2[/tex]
The alternative hypothesis is Hₐ; [tex]\hat{p}_1 \neq \hat{p}_2[/tex]
Where:
[tex]\hat{p}_1[/tex] = The proportion of the sample that did not use vitamin and had autism
[tex]\hat{p}_2[/tex] = The proportion of the sample that used vitamin and had autism
The test statistics for the difference of two proportions is given as follows;
[tex]Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}\cdot (1-\hat{p}) \cdot \left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}[/tex]
Where;
n₁ = 181, n₂ = 302, [tex]\hat p_1 = \dfrac{111}{181}[/tex], [tex]\hat p_2 = \dfrac{143}{302}[/tex], [tex]\hat p = \dfrac{111 + 143}{181 + 302 } = \dfrac{254}{283}[/tex]
[tex]The\ test\ statistics,\, Z=\dfrac{\dfrac{111}{181}-\dfrac{143}{302}}{\sqrt{ \dfrac{254}{283}\cdot (1-\dfrac{254}{283}) \times \left (\dfrac{1}{181}+\dfrac{1}{302} \right )}} \approx 2.98[/tex]
The test statistic for the test, Z ≈ 2.98
From the Z-table, we have Z > 2.98 = 1 - 0.9986, therefore, given that the
alternative hypothesis [tex]\hat p_1 \neq \hat p_2[/tex], the p-value is 2 × (1 - 0.9986) = 0.0028
The p-value associated with the test is 0.0028
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Find the equation of the line through the points (−2,5) and (4,9).
Enter your answer in standard form Ax+By=C, where A is a positive integer, and B and C are integers.
9514 1404 393
Answer:
2x -3y = -19
Step-by-step explanation:
Taking the differences between the given points, we have ...
(Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)
The equation of the line can be written ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line
4x -6y = 4(-2) -6(5) = -38
Dividing by 2 gives the standard form equation ...
2x -3y = -19
_____
Additional comment
The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."
Fishing Hook G is let down 2 times its present depth. Where is Fishing Hook G?
Answer:
[tex]2g[/tex]
Step-by-step explanation:
In other words, this problem is asking where Fishing Hook G is after it's 2 times deeper. Let g = its previous depth. We do 2 * g = 2g.
Last winter, the ratio of days with snow to days with no snow was 1.12. Write this ratio as a fraction in simplest form? PLS HELP
9514 1404 393
Answer:
28/25
Step-by-step explanation:
To make the number into a fraction, multiply and divide by 100:
1.12 × 100/100 = 112/100
Recognize that numerator and denominator have a factor of 4 in common:
112/100 = 28×4/(25×4) = 28/25
-3x + y = 10
solve the equation for Y
Answer:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-3*x+y-(10)=0
Pull out like factors :
-3x + y - 10 = -1 • (3x - y + 10)
Can anyone help please:)
Answer:
THEORTICAL PROBABILITY:
1A) F
1B) B
1C) A
1D) D,E,F
2A) R
2B) B
3A) odd number
3B) No, same.
3C) less than 5
================
1A) 8/30=4/15
1B) 10/30=1/3
1C) 12/30=2/5
1D) 18/30=3/5
1E) 22/30=11/15
1F) 22/30=11/15
2A) 3/8
2B) 1/8
2C)4/8=1/2
2D) 5/8
2E)3/8
3A) 50
3B) 150
3C) 250
3D) 100
3E) 100
Step-by-step explanation:
A 24-pack of mini cans of soda cost $21.98. How much iseach can?
Jacob went bowling over the weekend. On Saturday, he bowled at Bowlero, where he
rented shoes for $3.25 and paid $3.75 for each game. On Sunday, he bowled at the
Cowtown Bowling Center, where he rented shoes for $2.50 and paid $4.00 per game.
If he spent the same amount each day, how many games did he bowl? (Let the
number of games played = 2.)
Answer:
3 games played every Day
Step-by-step explanation:
So for Cowtown Bowling Center the cost of shoes is $2.50, and $4.00 per game
Then the Bowler is $3.25 for shoes and 3.75 per game
So to get the answer your gonna wanna set up the equation like
Saterday =$3.25+$3.75(x), then for
Sunday = $2.50+$4.00(x)
The X is how many games so if you plug in the same amount of game in both
Example
Saterday=$3.25+$3.75(2)=$10.75
Sunday = $2.50+$4.00(2)=$10.50
So if you do 3 then the totals will come out to be the same
Answer
Saterday=$3.25+$3.75(3)=$14.50
Sunday = $2.50+$4.00(3)=$14.50
I'll give brainliest please help
graphing
both of them please
Step-by-step explanation:
It's easier to graph when both equations are in its slope-intercept form, y = mx + b.
System 1: -3x -15y = 15-2x -10y = 10-2x -10y = 10
-2x + 2x - 10y = 2x + 10
-10y = 2x + 10
-10y/-10 = (2x + 10)/-10
y = -1/5x -1 [slope: -1/5, y-intercept (0, -1)]
-3x -15y = 15
-3x + 3x - 15y = 15
-15y = 3x + 15
-15y/-15 = (3x + 15)/-15
y = -1/5x - 1 [slope: -1/5, y-intercept (0, -1)]
To graph this system, plot the y-intercept, (0, -1) on the graph, then use the slope, m = -1/5 (down 1 unit, run 5 units to the right). Repeat the process until you have enough points to connect and create a line.
Because the given systems of linear equations are equivalent, their lines coincide on top of each other. This means that they have infinitely many points of intersection. Hence, they have infinite solutions.
System 2: 8x + 6y = 244x + 3y = 98x + 6y = 24
6y = -8x + 24
6y/6 = (-8x + 24)/6
y = -4/3x + 4 [slope: -4/3, y-intercept (0, 4)]
4x + 3y = 9
3y = -4x + 9
3y/3 = (-4x + 9)/3
y = -4/3x + 3 [slope: -4/3, y-intercept (0, 3)]
Use the same techniques as described in the first part. Plot the y-intercepts on the graph, then use the slope of each equation to plot other points.
These lines are parallel, which implies that they will never intersect each other. Hence, there's no solution to this system.
Attached are the screenshots of the graphed systems of linear equations.
Please help Please help Please help Please help Please help Please help
Answer:
the answer is b
Step-by-step explanation:
If someone build a house for 50 years how many months did it take to complete
Answer: 600
Step-by-step explanation: 12 months in one year. 12x50=600 months
Answer:
600 months
Step-by-step explanation:
In 1 year there are 12 months, so we take 50 (the years) and multiply that by 12
50x12=600 and we fact check by 600÷12=50. It takes 600 months to build the house over 50 years.
A line passes through the point (6,-4) and has a slope of - 4/3.
Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
In point-slope form,
y - y1 = m(x - x1)
m = -4/3
x1 = 6
y1 = -3
y + 3 = (-4/3)(x - 6)
What’s the answer to this question
Answer:
-9 and -8 ...............
Clayton wants to be a musician. After school one afternoon, he spends half his time practicing his drums and 3/4 of the remaining time on homework and dinner. He spends the remaining 3/4hour talking with and texting his friends. How long did he practice the drums?
Answer:
x - x/2 - (x/2)(3/4) - 3/4 = 0
x = 6
so, he spent 3 hours on the drums.
What is the x intercept of f(x) = x + 12
Answer:
-12
Step-by-step explanation:
Are the ratios of 3 apples to 5 oranges and 9 apples to 15
oranges equivalent? Why or why not? Explain
Answer:
yes they are equivelant
Step-by-step explanation:
the reason they are equivelant is because they go from 3 apples to 6 apples to 9 apple, and 5 oranges to 10 oranges to 15 oranges. so this mark's it is also tymced by three
Solve for h in the mathematical formula A=1/2(a+b)h
Step-by-step explanation:
Since we arent given enough information to SOLVE for h, I will get as close as I can by rearranging the equation for h
Convert the fraction to a decimal for simplicity
A = 0.5(a + b)h
Divide both sides of the equals by 0.5
A/0.5 = (a + b)h
We can convert A/0.5 into its reciprocal
2 A = (a + b)h
Divide both sides of the equation by the bracketed (a + b)
(2 A) / (a + b) = h
Rewritten
h = [tex]\frac{2A}{(a + b)}[/tex]Please help me with this problem.
Answer:
yes
no
yes
no
Step-by-step explanation:
You can tell it's negation when the word "not" is used.
Help me please express the simplest radical form
Answer:
The answer is 8√2
Hope this helps
Use the 1st derivative test to find the intervals where the function is increasing or decreasing. Please show your work so I can get a better understanding on how you achieved the solution. Thank you.
As the name of the test suggests, you have to compute the derivative:
[tex]f(x) = \dfrac1{2x+3} \implies f'(x) = -\dfrac2{(2x+3)^2}[/tex]
Find where, if at all, the derivative vanishes or is undefined - these are the critical points of f(x).
In this case, the derivative is never 0 since the numerator is constant and the denominator is non-negative. You also see that f '(x) is negative over its entire domain.
The denominator goes to 0 when 2x + 3 = 0, or x = -3/2.
Now split up the domain of f(x) into intervals with endpoints at the critical points. Here, we consider the two intervals, (-∞, -3/2) and (-3/2, ∞).
Take any point from either interval and check the sign of f '(x) at that point. Any points will do, but you should strive to pick one that makes calculations simple.
• From (-∞, -3/2), take x = -2; then f ' (-2) = -2 < 0. Since f '(x) is negative over this interval, f(x) is decreasing over it.
• From (-3/2, ∞), take x = 0; then f ' (0) = -2/9 < 0. Again, this means f(x) is decreasing over this interval.
So, the first derivative test tells us that f(x) = 1/(2x + 3) is decreasing over the intervals (-∞, -3/2) and (-3/2, ∞); in other words, over its entire domain.
For the second function, we have
[tex]f(x) = \dfrac{x+1}{x+3} \implies f'(x) = \dfrac{(x+3)-(x+1)}{(x+3)^2} = \dfrac2{(x+3)^2}[/tex]
Again, there's only one critical point, this time at x = -3 where the derivative is undefined.
• From the interval (-∞, -3), take x = -4; then f ' (-4) = 2 > 0, so f(x) is increasing.
• From the interval (-3, ∞), take x = 0; then f ' (0) = 2/9 > 0, so f(x) is increasing.
Is (–2, –9) a solution to the equation y = x + 7
Answer:
no
Step-by-step explanation:
Find the slope intercept form of the equation of the line that’s has the given properties (1 , 3) m=1/4
Answer:
y = 1/4x + 11/4
Step-by-step explanation:
Given the slope, m = 1/4, and the point, (1, 3):
We can substitute these values into the slope-intercept form, y = mx + b, in order to solve for the y-intercept.
The y-coordinate (b) of the point, (0, b ) is the y-intercept of the line where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.
y = mx + b
3 = 1/4(1) + b
3 = 1/4 + b
Subtract 1/4 from both sides:
3 - 1/4 = 1/4 - 1/4 + b
11/4 = b
The y-coordinate, b, of the y-intercept is 11/4.
Therefore, the slope-intercept form is: y = 1/4x + 11/4
Please mark my answers as the Brainliest if you find this explanation helpful :)
Explain the three different ways of writing a ratio and provide an example
Answer: The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6."
Step-by-step explanation:
you can write ratios as 3/6 , 3 to 6, or 3:6
Evalute: -|-x+2| for x = -3
Please help
Explain the significant of the arithmetic
modulo in solving problems then support your answer with examples.
Answer:
A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Simple addition would result in 7 + 8 = 15, but clocks "wrap around" every 12 hours.
Step-by-step explanation:
hope It's can help
If you can answer this right i'll mark you brainiest
Answer:Think of the equation as an equation for a line
y=mx+b
where in this case
C= 5 /9 (F−32)
or
C= 5 /9 F - 5/9 x 32
You can see the slope of the graph is 5 /9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5 /9 of 1 degree Celsius.
C= 5 /9 (F)
C= 5/9(1)
C=5/9
Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9/5 degrees Fahrenheit.
C= 5/ 9 (F)
1= 5 /9 (F)
(F)= 9 /5
Since
9/5 = 1.8, statement II is true.
The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of 5/9 degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:
C= 5 /9 (F)
C= 5 /9 x 5/9
C=25/81
(which is≠1)
An increase of 5/9
degree Fahrenheit leads to an increase of
25/81.
, not 1 degree, Celsius, and so Statement III is not true.
The final answer is D.
The number of hours Darla baby - sat her sister each week for the last 12 weeks is shown below
Answer: the box and whisker plot looks like this, the pink line starts between 8 and 10, the box starts between 10 and 12, the middle is between 14 and 16, the right side of the box is between 18 and 20, and lastly the pink line on the right ends at 22.
Step-by-step explanation: I did the test
Help I was absent when she taught this
Answer:
b
Step-by-step explanation:
) What is 35% of 10?
0.35(10)
Answer:
3.5
Step-by-step explanation:
35% of 10 is the same thing as 0.35(10)
0.35 x 10 = 3 + (0.05 x 10) = 3 + 0.5 = 3.5
-Chetan K
A gallon of apple juice is
$7. A pack of eight 4.23
oz box apple juice is
$2.39. Which is a better
deal?
Patricia visited a friend who lives 120 miles away. On her way there she averaged 60 mph. On the way back, she only averaged 40 mph. What was the total amount of time she spent driving?
Answer:
5 hours
Step-by-step explanation:
120/60= 2
120/40= 3
3+2=5