Using the z-distribution, it is found that she should take a sample of 46 students.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:
[tex]6\sigma = 800 - 200[/tex]
[tex]6\sigma = 600[/tex]
[tex]\sigma = 100[/tex]
The sample size is n when M = 29, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]29\sqrt{n} = 196[/tex]
[tex]\sqrt{n} = \frac{196}{29}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]
n = 45.67.
Rounding up, a sample of 46 students should be taken.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
12. If AC=4 and CD=4 13 in the figure below, what is cos x? B 45 45° А Xº D A. 2 13 B. 3 12 C. 2 13 D. 2 E. 1 4 C С 4-13
Answer:
c
Step-by-step explanation:
Mia read x pages in the book. Laurie read 1/3 more than that
Step-by-step explanation:
Laurie read x+1/3 pages.
Mia read x pages.
What is the area of a circle with a radius of 4 inches? Use 3.14 for π. Enter your answer as a decimal in the box.
enter your answer
in²
Answer:
A≈ 50.27in^2
Step-by-step explanation:
A= πr^2=
π·4^2≈ 50.26548
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
Required:
a. State the hypothesis 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?
d. What is the 95% confidence interval estimate of the difference between the two population proportion?
Answer:
The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.
Step-by-step explanation:
Let p1 be the sample of 1000 adults chosen in 2012 and
p2 be the sample of 1100 adults chosen in 2010
Part a:
The hypothesis that can be used to test for a significant difference between the population proportions for the two years is:
H0: p1-p2= 0 against the claim Ha: p1-p2≠0
Part b:
The sample proportion indicating that their financial security was more that fair in 2012 is
p1^= 410/1000= 0.41
In 2010 is:
p2^= 385/1100= 0.35
Part c:
p^c= 410+385/1000+1100= 0.3785
q^c= 1-p^c= 1-0.3785= 0.6124
The critical region is z > ±1.96
The test statistic is
z= p1^- p2^ / sqrt ( p^cq^c( 1/n1+ 1/n2)
z= 0.41-0.35 /sqrt( 0.3785*0.6124(1/1000 +1/1100)
z= 0.06 / 0.021036
z= 2.85
Conclusion
The calculated z = 2.85 falls in the critical region z > 1.96 so we accept the null hypothesis that there is no difference between the population proportions for the two years.
P- value : 0.00466
The result is significant( accept the null hypothesis) for value less than 0.05
Part d:
2012 2010
Sample 1000 1100
Proportions 0.41 0.35
Standard Error √0.41( 0.59)/1000 √0.35( 0.65)/1100
= 0.0155 0.01438
Standard Error for the difference = √0.0155² + 0.01438² =0.0211
p1-p2 ± z* standard error for the difference
0.41-0.35 ± 1.96 *( 0.0211)
0.06 ± 0.041356
-0.018644, 0.101356
The 95 % confidence interval estimate is (-0.018644, 0.10135
5 - x/3 for x = -3
Evaluate the expression
Anyone need help? :D
Answer:
yeah why? are you going to help?me
Answer:
Yes i actually do.
Step-by-step explanation:
NEED HELP WITH FUNCTIONS
Answer:
#############################
An 18 fluid ounce bottle of lotion costs $10.99, what is the price per fluid ounce?
Answer:
$0.61 per fluid ounce
Step-by-step explanation:
$10.99 / 18 = $0.61 per fluid ounce
how can you
change the equation y = mx + b to
shift the graph down?
Step-by-step explanation: To shift the graphs up and down on the coordinate system, you need to manipulate or change the y-intercepts.
The y-intercept is just the constant term in the equation.
As long as the slopes remain the same, the graphs can be
translated up or down by changing the constant value.
Take a look at these lines graphed below.
Notice that y = x + 11 is the same as y = x + 4 but
y = x + 11 is translated 7 units down to get y = x + 4.
Darlene's cat had a litter of southern kittens Three of the kittens were black what fraction of the kittens were not black also right this fraction into a division problem
Answer:
1/4
Step-by-step explanation:
48/96 in its simplest form
Answer:
1/2
Step-by-step explanation:
just divide it I guess
1/2
48/2
=24/2
=12/2
=6/2
=3
Hope this helps :D
Find the standard deviation of the given data rounded to the nearest hundredth, 147,141,120,124,128
Answer:
The correct answer is 10.30
Step-by-step explanation:
First, find the mean of the numbers by averaging them. Then, subtract the observation from the mean. Square them, then average them. Find the square root of this number and round to the nearest hundredth.
Answer:
10.30
Step-by-step explanation:
PC
You deposit $200 in an account that earns 4% simple interest. How much interest did you earn in 3 years? (Hint: I = prt)
Answer:
$24.
Step-by-step explanation:
Given that I deposited $ 200 in an account that earns 4% simple interest annually, to determine how much interest did I earn in 3 years, the following calculation must be performed:
((200 x 4/100) x 3) = X
((800/100) x 3) = X
(8 x 3) = X
24 = X
Thus, after 3 years of investment I will have earned $ 24 in interest.
If the simple interest on $2,000 for 2 years is $280, then what is the interest rate?
Answer:
0,28percent
Step-by-step explanation:
If simple interest formula is = P X r X t
Then interest rate = p X t/ I
angle DGF = ________
Answer:
65°
Step-by-step explanation:
[tex] m\angle DGF = 90\degree - 25\degree [/tex]
[tex] m\angle DGF = 65\degree [/tex]
Answer:
65
Step-by-step explanation:
Angle AGF = 90 (given)
Angle AGC = 25 (given)
Angle BGD = 25 (Vertically Opposite Angles are equal)
Angle DGF = 180-(90+25) (angles in a straight line is equal to 180)
=180-115
=65
Hope it helped!
Thanks!
find the area of ABC
Answer:
area of ABC=1/2 b×h=1/2×20×6=30m²
Answer:
60 m^2
Step-by-step explanation:
( Base * Hight / 2 = Area)
20 * 6 = 120
120 / 2 = 60
I don't know how to solve this problem
Before you read this!! To me, it looks like 8 is the entire length of lineJL, but it may only be the length of lineJM. I've written the steps for lineJL=8 NOT lineJM=8. If this is not the case and 8 is only the length of lineJM let me know so I can fix my answer!
Step-by-step explanation:
The area of a triangle is A=1/2(b)(h)
B=base
H=height
Your height is found in the line in the middle of the triangle, for you it is 6.
The base is the long bottom line on the triangle (lineJL), for you it is 8.
So let's put it in.
A=1/2(8)(6)
A=24sq units (C)
16 Which equations represent a relationship where у
is a nonlinear function of x? Select all that apply.
A. y= 4x
B. x = - 6y
C. y = |x| + 1
D.
y=2+1
х
E. x - 5y = 2
F.
1 1
y = +
Answer:
b
Step-by-step explanation:
5x - 4 = 2 (x + 3) + x
Step-by-step explanation:
5x - 4 = 2x + 6 × x
-----> 5x-3x = 6 + 4
-----> 2x = 10
----> x = 5
A random sample of 1175 people in a certain country
Answer:
c
Step-by-step explanation:
..........................
what is the difference between a quadratic function and a quadratic equation
Answer:
The roots of a quadratic equation simply tell what values of x will make the equation true. A quadratic function is a function where the largest power for the variable is 2. ... A quadratic equation is given to you so that you can solve it for the variable. A quadratic function is given to you so that you can graph it.
If a well is dug at -60 feet per day. How many days did it take to dig -5400 feet?
(Answer numerically ex: 30 Days answer = 30)
Answer:
90 days
Step-by-step explanation:
This one is just simple division, so you divide the goal number which is -5400 by -60 but in this situation you can just make them positives.
Find AB.
MN=22
DC=29
Answer:
AB=15
Step-by-step explanation:
Since DM =MA and CN=NB, then DC || MN || AB
29-22=7
22-7=15
AB=15
The cost of a tablet after a 20% discount can be represented by the expression t-0.2t. Simplify the expression
Step-by-step explanation:
simplified 0.16t I used a simplify calculator
- 3x + 5y = -2
2x - 2y = 1
Solve by elimination
the answer i think its 8 not sure
MONTRESOR: My dear Fortunato, you are luckily met. How remarkably well you are looking to-day! But I have received a pipe of what passes for Amontillado, and I have my doubts.
FORTUNATO: How? Amontillado? A pipe? Impossible! And in the middle of the carnival!
MONTRESOR: I have my doubts, and I was silly enough to pay the full Amontillado price without consulting you in the matter. You were not to be found, and I was fearful of losing a bargain.
FORTUNATO: Amontillado!
MONTRESOR: I have my doubts.
FORTUNATO: Amontillado!
MONTRESOR: And I must satisfy them.
FORTUNATO: Amontillado!
MONTRESOR: As you are engaged, I am on my way to Luchesi. If any one has a critical turn, it is he. He will tell me—
FORTUNATO: Luchesi cannot tell Amontillado from Sherry.
MONTRESOR: And yet some fools will have it that his taste is a match for your own.
FORTUNATO: Come, let us go.
MONTRESOR: Whither?
FORTUNATO: To your vaults.
Answer:
Montresor is luring Fortunato to a trap.
Step-by-step explanation:
Montresor is luring Fortunato to a trap that Montresor has prepared in his own basement.
In the story by Edgar Allen Poe, Montresor (the narrator) tells the reader that Fortunato has horribly insulted Montresor and Montresor will get revenge.
49 +
6. Luisa bought 23 pounds of apples,
3 pounds of oranges, and 14 pound
of pears. How many pounds of fruit
did she buy in all?
Answer:
23+3+14=40
Step-by-step explanation:
brainliest pls?
50 pounds to be exact
Find the area of the regular polygon. Round to the nearest tenth.
Given:
The figure of a regular polygon.
To find:
The area of the regular polygon.
Solution:
From the given figure it is clear that the regular polygon has 4 vertices. It means, it is a square.
Distance between the center and the vertex is 7 yd. So, the diagonal of the square is
[tex]d=7+7[/tex]
[tex]d=14[/tex] yd
We know that, area of a square is
[tex]A=\dfrac{1}{2}d^2[/tex]
Putting d=14 in the above formula, we get
[tex]A=\dfrac{1}{2}(14)^2[/tex]
[tex]A=\dfrac{1}{2}(196)[/tex]
[tex]A=98[/tex]
Therefore, the area of the regular polygon is 98 sq. yd.
One side, in inches, of a triangle is 5 more than twice a number. If this is an equilateral
triangle, what is the perimeter ?
Definition of an equilateral triangle: A triangle with the exact same sides and angles, which is 60°
5 more than twice a number:
Let the number be x:
2x + 5
Since it is an equilateral triangle, multiply that by 3:
3(2x +5) = 6x + 15
The perimeter is (6x + 15) inches.
5
A line passes through the point (4, -3) and has a slope of
4
Write an equation in slope-intercept form for this line.
Answer:
y = 4x -19
Step-by-step explanation:
y = 4x + b
first we add the point to the equation and then we solve for b
-3 = 4 ( 4 ) + b
-3 = 16 + b
-16
-19 = b