all real numbers except the 90 and 270 because of cosx
In a clinical trial of a certain drug, 17 subjects experience headaches among the 221 subjects treated with the drug. Construct a 95% (Wald) confidence interval estimate for the proportion of treated subjects who experience headaches.
a. Find the best point estimate of the population proportion.
b. Identify the value of the margin of error E.
c. Construct the confidence interval.
d. write a statement that correctly interprets the confidence interval.
Solution :
Given :
n = 221
x = 17
a). [tex]$p=\frac{17}{221}$[/tex]
= 0.076
b). At the 95 confidence interval
Value of z = 1.96
Margin of error
[tex]$=1.96 \times \sqrt{\frac{p(1-p)}{n}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076(1-0.076)}{221}}$[/tex]
[tex]$=1.96 \times \sqrt{\frac{0.076\times 0.924 }{221}}$[/tex]
= 1.96 x 0.017
= 0.03332
c). confidence interval
= ( 0.076-0.033, 0.076+0.033)
= ( 0.043, 0.109 )
d). The confidence interval does not contain null value, so it is significant.
Solve the following equation for
b
b. Be sure to take into account whether a letter is capitalized or not.
Answer:
b = h*D +hg^3
Step-by-step explanation:
b/h = D +g^3
Multiply each side by h
h* b/h = h*D +hg^3
b = h*D +hg^3
Help please guys thanks
Answer:
C
Step-by-step explanation:
the answer is C because only C contained it's correct root and power
What three consecutive integers equal -87?
Answer:
What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.
Step-by-step explanation:
Consecutive integers are as simple as 1, 2, 3!
Integers are consecutive if one follows another. How do we "jump" from one integer to the next? We add 1, right? 7, 8 and 9 are three consecutive integers. Add one to 7 to get 8 and add one more to get 9.
Now lets think about this in algebraic terms. Lets name these consecutive integers , x, y and z.
The problem tells us that their sum is -87. (Recall, "sum" is just a fancy word for the answer when we add.)
x+y+z = -87
Here is the trick! We need to rewrite this equation so that we have only one variable. Easy!
y is one more that x, so y= x+1
And z is one more than y, so z= y+1. But y is also equal to (x+1)! So z=y+1=(x+1)+1=x+2
Now we have a problem that we can solve! x+(x+1)+(x+2)=-87.
Combining term.: 3x+3=-87
Subtract 3 from both sides of the equation: 3x=84
Divide each side of the equation by 3: x=28
We have solved for x, but we are not done! We need to find y and z. I know you can do this. Remember y is one more than x and z is one more than y.
Check your work! Make sure these three consecutive numbers do in fact add up to -87.
Ed decides to include more fruit in his diet. He goes to the grocery store over the weekend and buys 6 apples, 6 oranges, and 6 avocados. The total cost is $19.50.
Ed finishes the apples very quickly, and has some leftover avocado. The following weekend he buys 12 apples, 2 oranges, and 1 avocado. This time he pays just $9.50.
The following week, Ed reads an article on the benefits of avocado, so over the weekend he buys 5 avocados along with 2 apples and 4 oranges. His total this time is $14.
Assume that Ed pays a unit price rather than a price per pound for the apples, oranges, and avocados.
9514 1404 393
Answer:
apples: $0.50 eaoranges: $0.75 eaavocados: $2.00 eaStep-by-step explanation:
Let a, o, v represent the prices of one each of apples, oranges, and avocados, respectively. Then the equations describing the purchases can be written ...
6a +6o +6v = 19.50
12a +2o +1v = 9.50
2a +4o +5v = 14.00
__
Dividing the first equation by 6 makes it ...
a +o +v = 3.25
Subtracting this from the second equation gives ...
(12a +2o +v) -(a +o +v) = (9.50) -(3.25)
11a +o = 6.25
Subtracting the third equation from 5 times the reduced first equation gives ...
5(a +o +v) -(2a +4o +5v) = 5(3.25) -(14.00)
3a +o = 2.25
The difference of these last two equations is ...
(11a +o) -(3a +o) = (6.25) -(2.25)
8a = 4.00
a = 0.50
Then the other values are ...
o = 2.25 -3(a) = 0.75
v = 3.25 -a -o = 2.00
The unit prices are:
apples -- $0.50
oranges -- $0.75
avocados -- $2.00
_____
Additional comment
Most graphing or scientific calculators will solve systems of equations like these. Using an appropriate tool, it takes less time to find the solution than to read this one.
Note that the last purchase description in the problem statement has the items in a different order than in the first two descriptions. Care must be taken to make sure the correct equations are written.
Which equation describe the line through the points (2,-4) and (5,8)
Answer:
Your equation would be
y=4x-12
Step-by-step explanation:
So an easy way to figure this out is graph the points and look at the distance the points are away from each other. In this case it was 12 up and 3 right. This is your slope. Simplify the fraction to 4/1. Then from (2,-4) use the given slope to work back to a point that is on the y axis, which is (0,12). Plug all of the given information you found into y=mx+b and you get the given formula.
Multiply (2x-5)(x+3)
Answer:
2x^2+x-15
Step-by-step explanation:
foil
Answer:
2x^2 + x - 15
Step-by-step explanation:
using FOIL
(2x - 5)(x + 3)
[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]
[2x^2 + 6x - 5x - 15]
2x^2 + x - 15
A fisheries biologist has been studying horseshoe crabs. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is
where the deviations ε i are assumed to be independent and Normally distributed with mean 0 and standard deviation σ . This model was fit to the data using the method of least squares. The following results were obtained from statistical software:
R 2 =0.423, s=2.2018
The quantity s = 2.2018 is an estimate of the standard deviation, σ, of the deviations in the simple linear regression model. The degrees of freedom for s are
a.) 100
b.) 99
c.) 98
d.) 2
Answer:
C. 98
Step-by-step explanation:
The proposed regression equation is weight = b + width * m
R2 = 0.423
A.) What is the regression equation for this example?
The estimate for the y-intercepts is b= 2.3013 and the estimate for the slope is m= 0.7963
In general, we can symbolize the estimated regression equation as ^Y= b + m*Xi. For this example you have to replace it with the calculated values of the regression coefficients to obtain the estimated regression equation:
^Y= 2.3013 + 0.7963Xi
B.) What is the explanatory, or predictor, variable in this study?
The explanatory or predictor variable is the variable that is suspected to have an effect over the response variable. In this example the predictor variable is:
X: Width of a horseshoe crab (cm)
C.) If the researcher wanted to test whether there is a statistically significant relationship between these two variables, what would the test statistic be? Calculate it from the table above.
To test if the regression is significant, the parameter of study will be the slope of the regression equation, symbolically: β. If the slope is equal to zero "β=0" then there is no linear regression between the response and explanatory variable. If the slope is different from zero "β≠0" then the regression is significant and the explanatory variable affects the response variable.
The hypotheses are:
H₀: β=0
H₁: β≠0
α: 0.05
The value of the statistic under the null hypothesis is t= 8.48
D.) What can we say about the p-value?
This test is two-tailed and so is the p-value, remember that the p-value is the probabulity of obtaining a value as extreme as the value of the statistic under the null hypothesis. The distribution for this test is a t with n-2= 100-2= 98 degrees of freedom. You can calculate the p-value as:
P(t₉₈≤-8.48) + P(t₉₈≥8.48)= P(t₉₈ ≤ -8.48) + (1 - P(t₉₈ < 8.48) ≅ 0.00001
E.) Ultimately, the reason that we find test statistics is so that we can compare them to a null distribution. For regression, that is a t-distribution based on the degrees of freedom. With 98 degrees of freedom (100-2), we can safely say that the critical t (or the confidence multiplier) is what?
As mentioned before, this test is two tailed, meaning that the rejection region is divided in two:
Critical values ± = ± = ± 1.984
This means that you'll reject the null hypothesis when the statistic is t ≤ -1.984 or if the statistic is t ≥ 1.984-
F.) Find the confidence interval for the slope.
Using a 95% confidence level, the interval for the slope is:
[m ± Sm]
[0.7963 ± 1.984 * 0.0939]
[0.61; 0.98]
G.) Is there a statistically significant relationship? Answer with the test statistic and the confidence interval.
Yes, there is a significant relationship between the width and weight of the horseshoe crabs.
Using the critical value approach:
The calculated statistic is 8.48 and the critical value is ± 1.984, since the statistic is greater than the positive critical value, the decision is to reject the null hypothesis.
If you pay attention to the confidence interval, which was made at a confidence level complementary to the significance level of the hypothesis test, this interval [0.61; 0.98] doesn't include the "zero". Since the interval doesn't include the value of the parameter stated in the null hypothesis, you can conclude that this hypothesis is not true and therefore reject it.
Evaluate the expression when x = 12/7
The value of the expression when x equals is ???
PLEASE HELP!!
Answer:
82
Step-by-step explanation:
1/3( x+9/7) + 3^4
Let x = 12/7
1/3( 12/7+9/7) + 3^4
PEMDAS says parentheses first
1/3( 21/7) + 3^4
1/3(3) +3^4
Then exponents
1/3(3)+81
Then multiply
1+81
82
For each kilogram of a persons weight 2.5 milligrams of a drug is to be given. what dosage should be given to a child who weighs 84 pounds? Use the fact that 1 lb = 0.45 kg
Answer:
A child who weighs 84 pounds should be given 94.5 milligrams of the drug.
Step-by-step explanation:
Givens:
1kg=2.5 milligrams of dosage
Weight of child = 84 pounds
1 pound = 0.45 kg
Solution:
Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg
Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.
Four seconds pass between the first and third flash of a strobe light. The rate at which the strobe flashes is constant. How many seconds will pass between the first and the twelfth flash of the same light?
Answer:
t = 22 s
Step-by-step explanation:
If n is the number of strobe pulses
The first strobe pulse occurs at t = 0
t = 2(n - 1)
t = 2(12 - 1)
t = 2(11)
t = 22 s
Miya is picking up two friends to go the beach. She drives from her house to
pick up Drea, then she drives to pick up Francine, and then they go to the
beach to play volleyball. What is the total distance of the trip?
The grid below shows the coordinates of their houses on a map. All distances
are in miles.
Answer:
Option (C)
Step-by-step explanation:
Coordinates of the point representing the location of Miya → (1, 10)
Coordinates of the point representing the location of Drea → (13, 1)
Coordinates of the point representing the location of Francine → (16, 1)
Coordinates of the point representing the location of Beach → (19, 4)
Distance between Miya and Drea = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(13-1)^2+(1-10)^2}[/tex]
= [tex]\sqrt{144+81}[/tex]
= 15 miles
Distance between Drea and Francine = [tex]\sqrt{(16-13)^2+(1-1)^2}[/tex]
= 3 miles
Distance between Francine and Beach = [tex]\sqrt{(19-16)^2+(4-1)^2}[/tex]
= [tex]\sqrt{9+9}[/tex]
≈ 4.2 miles
Total distance between Miya and the beach = 15 + 3 + 4.2
= 22.2 miles
Option (C) is the answer.
Vietnamese: Phát biểu định nghĩa hàm số liên tục. Khảo sát tính liên tục của hàm số sau:
Answer:
litrally I don't understand what you are telling
Pls if anyone knows the answer that will be greatly appreciated :) question 1 btw
Answer:
here's the answer to your question
Use the discriminant to determine all values of k which would result in the graph of the equation
y
=
3
x
2
+
k
x
+
75
y=3x
2
+kx+75 being tangent to the x-axis.
Answer:
sauce is 177013
Step-by-step explanation:
Please help with this while part!!!!
Step-by-step explanation:
1. The given expression is, [tex]A=lw[/tex]
We need to solve it for w.
[tex]w=\dfrac{A}{l}[/tex]
2. The given expression is, [tex]C=\pi D[/tex]
We need to solve it for D.
[tex]D=\dfrac{C}{\pi}[/tex]
3. The given expression is, [tex]v=s+gt[/tex]
We need to solve it for s.
[tex]s=v-gt[/tex]
4. The given expression is, [tex]5x-2y=11[/tex]
We need to solve it for y.
[tex]D=\dfrac{5x-11}{2}[/tex]
5. The given expression is, [tex]P_1V_1=P_2V_2[/tex]
We need to solve it for P₂. So,
[tex]P_2=\dfrac{P_1V1}{V_2}[/tex]
I don’t understand these 3 questions and I need help.
Answer:
1: A=1
2: -3
3: C
Step-by-step explanation:
1: If 3x+4 is a factor, then -4/3 is equal to x. Substitute it in for x and solve for a. This gives us A=1.
For the commenter not understanding how I got -4/3: 3x+4 being a factor means that it equals 0. It might help you understand this if you remember that after factoring, like I did for 38 in my photo, we take expressions like x-4 and set them equal to 0 to get x=4, a solution. So, subtract 4 from both sides to get 3x=-4, then divide both sides by 3 to get x alone. Thus, x=-4/3.
2: To find the sum, we first need to find the two solutions. We can factor to get (x+7)(x-4). This gives us x=-7 and x=+4. The solution of these two would be (-7)+4 is -3.
3: B is a close answer, but the signs are wrong on the bottom. Factoring the question would give us 2(x-2) / 2(x^2-x-2). Factoring that equation is 2(x-2) / 2(x+1)(x-2). Simplifying this gives us 1 / x+1.
Sorry for the bad penmanship, I wanted to make it a little clearer for you! I really hope I helped! :)
Write the equation of a line in slope intercept form that passes through the two points. 4,-1 and 6,-7
A line has an equation of,
[tex]y=mx+n[/tex].
m is called a slope
n is called y-intercept
We are also given two points [tex](x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7)[/tex].
We begin with computing the slope,
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}[/tex]
We have computed the slope m and our equation is almost done,
[tex]y=-3x+n[/tex]
Next step is to find out what y-intercept n is. I will use point [tex](4,-1)[/tex] and insert x and y it into already known equation, then solve for n,
[tex]-1=-3(4)+n[/tex]
[tex]-1=-12+n\implies n=\boxed{11}[/tex]
The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,
[tex]\boxed{y=-3x+11}[/tex]
Hope this helps. :)
Find how much money needs to be deposited now into an account to obtain $7,300 (Future Value) in 6
years if the interest rate is 2.5% per year compounded monthly (12 times per year).
The final amount is $
Round your answer to 2 decimal places
Answer:
x= $6,284.15
Step-by-step explanation:
7300 = x(1 + .025/12)^72
x = [tex]\frac{7300}{(1 + \frac{.025}{12} )^{72} }[/tex]
x= $6,284.15
4. Work out the area.
Answer:
90m^2
Step-by-step explanation:
image shows a trapezium,
area of trapezium = h(a+b)/2 = 9(8+12)/2 = 90
Answer:
29
12+8+9 =29
Step-by-step explanation:
additional question
add tose measure
Maria, Kevin, and Dan have a total of 96$ in their wallets. Dan has 6$ less than Maria. Kevin has 3 times what Dan has. How much do they have in their wallets?
Answer:
Hi Keke,
Let Amy have x dollars. Then Jose has x - 8 dollars and Milan has 4(x - 8) dollars.
x + (x-8) + 4(x-8) = 152
6x - 40 = 152
6x = 192
x = 32
Amy has $32
Jose has 32 - 8 = $24
Milan has 4*24 = $96
Identify the coefficients for the following quadratic equation.
2x squared minus 9x equals negative 4
a =
b=
c=
Answer:
2
Step-by-step explanation:
the number before the x² is regarded as the identity element
how would i find the area of the blue region and the perimeter of the outer window frame
Answer:
The diameter is 6. The radius is 3. For the half of the orange circle.
The area of the half of the small orange circle is = pi*r*r = pi*3*3.
The diameter is 24. The radius is 12.
The area of the half of the light orange circle and the other colors is = pi*r*r = pi*12*12
The area of dark orange, light blue, purple and green figures = pi*12*12 – pi*3*3 = 135*pi
To get the area of the blue figure we need to divide 135*pi into ¼ and you will get the area of the blue figure.
The area of the blue figure =( ¼ )*135*pi *(1/2) = ¼ *1/2 = 1/8
The area of the blue figure is = 135pi / 8
B) outside perimeter of the window frame = 28 +pi*14 = 71.98
Hope this helps you :)
Jim, Katrina, Larry, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim last?
c. Find the probability that Jim will arrive first and Kim last.
a.___ (Type an integer)
b.___ (Type an integer.)
c.___ (Type a fraction. Simplify your answer)
Answer:
24
6
1/12
Step-by-step explanation:
a) This is a counting problem 4*3*2*1 = 24 different ways.
b) 1 * 2 * 1 * 1 = 2 ways
This is one you should try.
Jim Kat Larry Kim
Jim Larry Kat Kim
You can't get another way.
c)
There are 2 ways that Jim can arrive first and Kim Last shown in b
2/24 = 1/12
Question 1 (Fill-In-The-Blank Worth 4 points)
(05.02)The area of the parallelogram below is
square meters
6 m
7 m
2 m
Numerical Answers Expected!
Answer for Blank 1
Step-by-step explanation:
we don't see the parallelogram nor any description of it.
so, it is impossible to tell you the right answer.
as I only answer questions by don't ask any, I don't know how you can add a picture.
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 50 m. (Round your answer to two decimal places.)
Answer:
2.75 m²
Step-by-step explanation:
From the information given:
the thickness of the paint = 0.07 cm = (0.07/100) m
= 0.0007 m thick
the diameter hemispherical dome = 50 m
∴
radius of the dome = 50m /2 = 25 m
The volume of a hemispherical dome is expressed as:
[tex]V = \dfrac{2}{3}\pi r^3[/tex]
Thus, the change in the volume now is:
[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]
[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]
[tex]{dV} = 2 \pi r^2 (dr)[/tex]
∴
dV = 2π × (25)² (0.0007)
where;
dr = 0.0007
dV = 2π × (25)² (0.0007)
dV = 2.75 m²
1/4 (2.6x+0.25)-5/8 (2.5-0.88x)
The given expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x) when simplified is 1.2x - 1.5.
To simplify the expression 1/4 (2.6x + 0.25) - 5/8 (2.5 - 0.88x), we'll apply the distributive property and combine like terms.
First, let's simplify the expression within the first set of parentheses:
2.6x + 0.25
Next, we multiply this expression by 1/4:
(1/4) * (2.6x + 0.25) = (2.6/4)x + (0.25/4) = 0.65x + 0.0625
Now, let's simplify the expression within the second set of parentheses:
2.5 - 0.88x
We'll multiply this expression by -5/8:
(-5/8) * (2.5 - 0.88x) = (-5/8)(2.5) - (-5/8)(0.88x) = -1.5625 + 0.55x
Finally, we can combine the simplified expressions:
0.65x + 0.0625 - 1.5625 + 0.55x = (0.65x + 0.55x) + (0.0625 - 1.5625) = 1.2x - 1.5
To learn more about expression click on,
https://brainly.com/question/29521689
#SPJ2
Complete question is:
Simplify the expression 1/4 (2.6x+0.25)-5/8 (2.5-0.88x)
[tex]2i+3x=4-ix[/tex]
Show work.
No wrong answers or you will be reported. I will mark Brainliest! Thank you!
Answer:
Step-by-step explanation:
I am assuming i is the imaginary number:
Factor:
(3 + i)x - (4-2i) = 0.
In order for this to equal 0, x must be equal to 1-i.
I don't want to be reported to so take my word for it.
Also I plugged it into wolfram alpha so if it is wrong, blame the most powerful math equation solver available on the internet.
Using BTS he properties, find the unit's digit of the cube of each of the following numbers
Player Productions theatre finds that their ticket sales for Friday night performances (number of tickets sold) is given by the function h , where h ( t ) measures the number of tickets sold, and where t is the play length (measured in hours). Regal Theatre found that their ticket sales for Friday nights performances can be modeled by the function, g , where g (t)= 1.6h(t + 0.25).
Required:
How do the ticket sales for Friday night perfomances at Player Productions compare to the ticket sales for a Friday night perfomance at Regal Theatre?
Answer:
Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions
Step-by-step explanation:
Given
[tex]h(t) \to[/tex] player production theatre
[tex]g(t) \to[/tex] regal theatre
Where:
[tex]g(t) = 1.6h(t + 0.25)[/tex]
Required
Compare both functions
We start from the bracket
[tex]t + 0.25[/tex]
The + in [tex]t + 0.25[/tex] means longer hours of production
So:
[tex]t + 0.25[/tex] means 0.25 hours longer that player productions
[tex]g(t) = 1.6h(t + 0.25)[/tex] can be rewritten as:
[tex]g(t) = 1.6 * h(t + 0.25)[/tex]
The above means 1.6 times player production when they have 0.25 longer hours.
Find the missing side lengths
Answer:
y=9 and x=9*sqrt(2)
Step-by-step explanation:
tan(45)=9/y, 1=9/y, y=9
sin(45)=9/x, 1/sqrt(2)=9/x, x=9*sqrt(2)
