Answer:
A sample of 595 should be obtained.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Estimate of 0.55
This means that [tex]\pi = 0.55[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04?
This is n for which M = 0.04. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.55*0.45}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96\sqrt{0.55*0.45}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.55*0.45}}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.55*0.45}}{0.04})^2[/tex]
[tex]n = 594.2[/tex]
Rounding up,
A sample of 595 should be obtained.
4(x + 1) – 2x = 5 – x , what is the value of x ?
Answer:
x=3
Step-by-step explanation:
4(x+1) -2x = 5-x
divid 4 by whats in parentheses
4x+4 -2x =5-x
combind 4x and -2x
2x+4=5-x
combind 2x and x
3x+4=5
subtract 4 from 5
3x=1
3÷3 and 1÷3
x=3
Answer:
x = 0.33
Step-by-step explanation:
4(x + 1) - 2x = 5 - x
4x + 4 - 2x = 5 - x
4x - 2x + 4 = 5 - x
2x + 4 = 5 - x
2x + x + 4 = 5 - x + x
3x + 4 = 5
3x = 5 - 4
3x = 1
3x ÷ 3 = 1 ÷ 3
x = 0.33
Mr and mrs smith buy tickets for themselves and their four children. the cost of an adult ticket is ? 6 more than the adult ticket. the total cost of the six tickets is ? 40.50 work out the cost of an adult ticket. in your working let c be the cost of the child ticket and a be the cost of the adult ticket.
Answer:
child's ticket = 4.75 adult ticket=10.75.
Step-by-step explanation:
The cost of an adult ticket is 6 more than that of a child ticket, so will be denoted by c+6. Now, we are told that the cost of four child tickets and two adult tickets is 40.50, so we can put this in an equation and solve for c:
(c+6)+(c+6)+c+c+c+c=40.50
6c+12=40.50
6c=28.50
c=4.75
Therefore the cost of a child's ticket (c) is 4.75 and the cost of an adult ticket (c+6) is 10.75.
Find the value of x.
(a)
(10.7)" = 2
3x92x1 = 27*
(b)
Step-by-step explanation:
where is x in the question
A racing car driver is investigating whether the type of fuel he uses in his car affects his overall speed. He uses three different types of fuel. The driver runs an experiment where he fills his car with each type of fuel 20 times, and each time records the time taken to drive one lap of a track. A one-way ANOVA test is conducted to test the null hypothesis that type of fuel is not a significant factor in determining speed. The result of the test is that the null hypothesis is not rejected.
The conclusion that follows from this test is that: __________
a. it has been proven that the type of fuel is a significant factor in determining speed
b. it cannot be ruled out that the type of fuel is an insignificant factor in determining speed
c. it has been proven that the type of fuel is an insignificant factor in determining speed
d. it has been proven that the type of fuel can sometimes be a significant factor in determining speed
Answer:
b. it cannot be ruled out that the type of fuel is an insignificant factor in determining speed.
Step-by-step explanation:
From the question :
Let the speed of each fuel be represented as ;
u1, u2, u3
The null hypothesis, H0 ;
H0 : u1 = u2 = u3
H0 is of the notion that fuel type is not a significant factor in determining speed
The alternative hypothesis, H1;
H1 : u1 ≠ u2 ≠ u3
The alternative is the opposite of the null, fuel type is a significant factor in determining speed
If after conducting the statistical test, the null hypothesis cannot be rejected ;
Then the conclusion will be ;
There is no significant evidence to conclude that the fuel type is a significant factor in determining speed ;
Hence, fuel fuel type remains an insignificant factor in determining speed.
Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.
sin(2sec^-1 u/10)
Answer:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
Step-by-step explanation:
We want to write the trignometric expression:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0[/tex]
As an algebraic equation.
First, we can focus on the inner expression. Let θ equal the expression:
[tex]\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)[/tex]
Take the secant of both sides:
[tex]\displaystyle \sec(\theta)=\frac{u}{10}[/tex]
Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:
[tex]\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}[/tex]
By substitutition:
[tex]\displaystyle= \sin(2\theta)[/tex]
Using an double-angle identity:
[tex]=2\sin(\theta)\cos(\theta)[/tex]
We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:
[tex]\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)[/tex]
Simplify. Therefore:
[tex]\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0[/tex]
What probability statement would you add to P(blue) = 1 10 to make a complete probability model for the event choosing a foam ball at random from the box?
Answer:
The chances of landing on blue are 1 in 4, or one fourth. The chances of landing on red are 1 in 4, or one fourth. This problem asked us to find some probabilities involving a spinner.
The function f is defined by f(x) = 57. What is the value of f(3)?
O 15
O 25
O 53
O 125
Answer:
53
Step-by-step explanation:
Because
Which fraction is equivalent to 2/-6
Answer:
-1/3
Step-by-step explanation:
The length of a rectangle is 3 inches more than three times it's width. Write an equation relating the length, “, of the rectangle to its width, w.
QUICK PLEASE I NEED HELP ON THIS
Answer:
Some
Step-by-step explanation:
the mean absolute deviation would intersect and would there for be some but at far enough apart to not be a lot
how do i solve for the inequality, p=3.4?
Answer:
Step-by-step explanation:
This is already solved, and this would not be considered a inequality since it has only a equal sign.
(see picture) Find the measures of the numbered angles in each isosceles trapezoid.
PLEASE HELP ASAP!!! URGENT
Verify the identity. Sinx/1-cosx = cscx+cotx
Please use the answers shown in the image !! Thank you !!
Answer:
1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex]
2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex]
3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex]
4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex]
5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex]
6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex]
7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex]
Step-by-step explanation:
Now we proceed to show all steps needed to demonstrate the trigonometric identity:
1) [tex]\frac{\sin x}{1-\cos x} = \csc x + \cot x[/tex] Given.
2) [tex]\frac{\sin x}{1-\cos x} = \frac{1}{\sin x} + \frac{\cos x}{\sin x}[/tex] Identities for cosecant and cotangent functions.
3) [tex]\frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x}[/tex] [tex]\frac{a}{b}+\frac{c}{b} = \frac{a+c}{b}[/tex]
4) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x \cdot (1+\cos x)}{\sin^{2}x}[/tex] Existence of additive inverse/Modulative property.
5) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{1-\cos^{2}x}[/tex] Fundamental trigonometric identity.
6) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x\cdot (1+\cos x)}{(1+\cos x)\cdot (1-\cos x)}[/tex] Factorization.
7) [tex]\frac{\sin x}{1-\cos x} = \frac{\sin x}{1-\cos x}[/tex] Existence of additive inverse/Modulative property/Result.
Someone please help me answer this!!
Answer:
a = 15yd is the answer.
Step-by-step explanation:
a = ?
b = 8yd
c = 17yd
By using the Pythagoras theorem,
a² + b² = c²
a² + 8² = 17²
a² + 64 = 289
a² = 289 - 64
a² = 225
a = 15
∴ a = 15yd is the length of the missing leg.
I just need help finding out the missing sides
find the least common multiple of 16,30,36 no links or file
9514 1404 393
Answer:
720
Step-by-step explanation:
The LCM of these numbers will have every factor that is part of these numbers.
16 = 2^4
30 = 2 × 3 × 5
36 = 2^2 × 3^2
So, the LCM will have factors of 2^4, 3^2, and 5:
LCM(16, 30, 36) = 2^4 × 3^2 × 5 = 720
720 = 16×45 = 30×24 = 36×20
The least common multiple is 720.
Please help!!
Imaginary Numbers
Answer:
A. 1
Step-by-step explanation:
its A
POSSIBLE POINTS: 6
Solve each equation and match the solution.
e+8=31
t−25=54
32=y −21
14=b−12
x+8.95=21.95
n +21 =32
Answers,
1. 23
2. 79
3. 53
4. 26
5. 13
6. 11
How I did this,
What I did was subtract 8 from 31 to get ( e ) by itself.
This subject will get harder so I reccomend you focus on school and learn how to do this.
Solve the system of equations.
2.5y+ 3x = 27
5x-2.5y = 5
What equation is the result of adding the two equations?
What is the solution to the system?
Answer:
The asnwer to the system of equation
x=4 y=6
Step-by-step explanation:
Answer: 1) 8x=32 2) (4,6)
Step-by-step explanation:
Hope this helps!
Mark me brainliest!
Pls and ty!
Question 20 A retired couple invested $6000 in bonds. At the end of one year, they received an interest payment of $402. What was the simple interest rate of the bonds?
Answer: interest rate was 6.7 %
Step-by-step explanation: 402/6000 = 0.067 = 6.7%
There were 816 cars parked in the parking lot on Monday morning. At lunchtime 91 cars left the lot. After lunch, 135 cars came back to the parking lot. How many parking spots were left on Monday morning ?
Answer:
467
Step-by-step explanation:
There were a total 1327 parking lots.
Out of these 816 were taken in the morning, 91 cars left in the afternoon, while 135 came back after lunch.
So there are,
[tex]Cars left = 1327 - (816 - 91 + 135) \\\\ = 1327 - 860\\ = 467[/tex]
Thus, there are 467 parking spots left on Monday afternoon.
An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
Answer
16/43
Step-by-step explanation:
17 Male + 27 female = 44 students
now n= 2 so first student was male so one male student was taken out of the equation so 16 male left. now left male students by remaining students so now total left students = 43
so, prob = remaining males/remaining students=16/43
xsquare-8x+15 please help me answer it thank you
Step-by-step explanation:
[tex] {x}^{2} - 8x + 15 = 0 \\ (x - 3)(x - 5) = 0 \\ x = 3 \: or \: x = 5[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each division expression with the correct quotient. (These are the answers)
18x^(2)+39x+15 over 3x+5 -----> 6x+3
35x^(2)-5x-30 over 5x-5 -------> 7x+6
15x^(2)-44x+21 over 5x-3 ------> 3x-7
Answer:
18x^(2)+39x+15 over 3x+5 -----> 6x+3
35x^(2)-5x-30 over 5x-5 -------> 7x+6
15x^(2)-44x+21 over 5x-3 ------> 3x-7
Step-by-step explanation:
Plato Gang
twice the difference of v and z
Answer:
me
Step-by-step explanation:
becaus im the bes guy
Help please question in picture
Answer:
220
Step-by-step explanation:
Area of square=8*20=160
Area of triangle=(6*20)/2=60
160+60
Answer:
220 units²
I'm sure this is the answer!
Help what is 3 1/2 divided by 8
help aced and expert giving 20 points
Only 3 more questions to go
Find cos(B) in the triangle.
Choose 1 answer: