Answer:
a) The 90% confidence interval on the proportion of such graduates planning to continue their education is (0.2097, 0.2737).
b) The 95% confidence interval on the proportion of such graduates planning to continue their education is (0.2036, 0.2798).
c) Due to higher value of z, a 95% confidence interval, as in part b, is wider than a 90% confidence interval, found in part a, and is the difference between these two intervals.
d) Yes, because 0.25 is inside both intervals.
Step-by-step explanation:
Question a:
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].
117 of 484 new engineering graduates were planning to continue studying for an advanced degree.
This means that [tex]n = 484, \pi = \frac{117}{484} = 0.2417[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 - 1.645\sqrt{\frac{0.2417*0.7583}{484}} = 0.2097[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 + 1.645\sqrt{\frac{0.2417*0.7583}{484}} = 0.2737[/tex]
The 90% confidence interval on the proportion of such graduates planning to continue their education is (0.2097, 0.2737).
Question b:
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].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 - 1.96\sqrt{\frac{0.2417*0.7583}{484}} = 0.2036[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 + 1.96\sqrt{\frac{0.2417*0.7583}{484}} = 0.2798[/tex]
The 95% confidence interval on the proportion of such graduates planning to continue their education is (0.2036, 0.2798).
(C) Compare your answers to parts (a) and (b) and explain why they are the same or different.
The margin of error of a confidence interval of proportions is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
This means that, due to higher value of z, a 95% confidence interval, as in part b, is wider than a 90% confidence interval, found in part a, and is the difference between these two intervals.
(D) Could you use either of these confidence intervals to determine whether the proportion is actually 0.25? Explain your answer. Hint: Use the normal approximation to the binomial.
Yes, because 0.25 is inside both intervals.
PLEASE HELP!! WILL MARK AS BRAIN LIST
Write the inequality shown by the graph
A catering company needs 8.75 Ib of shrimp for a small party. They buy 3 2/3 Ib of jumbo shrimp, 2 5/8 Ib of medium-sized shrimp, and some mini-shrimp. How many pounds of mini -shrimp do they buy?
Ali's dog weighs 8 times as much as her cat together the two pets weigh 54 lb how much does Ali's dog weigh
Answer:
48
Step-by-step explanation:
Cat = x
Dog = 8x
x + 8x = 54
9x = 54
x = 6, Dog = 8 * 6 = 48
May you please help me figure out every angle?
Answer:
<D = 82°
<E = 49°
<F = 49°
Step-by-step explanation:
This is an isosceles triangle because two of the sides are the same length which means the 2 bottom angles are the exact same which means we can set them equal to each other to solve for it.
Determine whether the following graph can represent a normal curve.
Could the graph represent a normal curve? Select all that apply.
Answer:
C
Step-by-step explanation:
A normal curve describes a unimodal curve... this has 2 peaks (bimodal)
**this looks like stats?**
The graph does not represent a normal curve since:
No, because the graph has multiple peaks.No, because the graph approaches the X-axis as X increases and decreases without bound.Graphically speaking, the probability density function of a normal distribution has the following characteristics:
It has a single "peak" at a value of [tex]x[/tex] associated to the mean.The function is distributed symmetrically.The y-value of the function tends to be zero when [tex]x \to \pm \infty[/tex].The curve presented in the image only observes the condition described in 2. Therefore, we conclude that correct choices are:
No, because the graph has multiple peaks.No, because the graph approaches the X-axis as X increases and decreases without bound.We kindly invite to check this question on normal curves: https://brainly.com/question/15992479
Rory earned an 84% on his test. He answered 21 questions correctly. How many total questions were on the
test? Round to the nearest tenth if necessary
Answer:
25 questions,
$18.75
Step-by-step explanation:
Remember, to change percents to decimals, divide the number by 100 and remove the parentheses.
1. 84%, or 21 questions of Roy's test were correct.
Let's set the number of questions on the test as "x". We can then write this equation:
84% * x = 21
Simplify.
0.84 * x = 21
Divide both sides by 0.84
x = 25
There were 25 questions on the test.
2. Cheesecake Factory question
We need to find 15% of 125.
15% * 125 =
0.15 * 125 =
18.75
They need to leave a $18.75 tip.
I hope this helps! Feel free to ask any questions!
Daniel is making cupcakes for a school bake sale. He wants to make 120 cupcakes. So far he has made 65% of them. How many more cupcakes does he need to make?
What is 35percent of 275
Answer:
iyou tell me
Step-by-step explanation:
Answer:
96.25
Steps:
35 × 275 / 100 = 9625 / 100 = 96.25
PLEASE HELP I DONT GET THIS ASAP! IS THIS 21??
A tank is draining water such that the volume is given which an exponentially decreasing graph as shown in the graph below. If the volume was modeled with an equation of the form V=a(b)^t, where t is the number of hours then which of the following is the best value for b?
(1) b=20
(2) b=0.6
(3) b=2.8
(4) b=0.3
Answer:
[tex]b = 0.3[/tex]
Step-by-step explanation:
Given
[tex]V = ab^t[/tex]
See attachment for graph
From the graph
V = 20 when t = 0
This implies that:
[tex]V = ab^t[/tex]
[tex]20 = ab^0[/tex]
[tex]20 = a * 1[/tex]
[tex]20 = a[/tex]
[tex]a = 20[/tex]
Also:
V = 4 when t = 1.5
So:
[tex]4 = ab^{1.5[/tex]
Substitute 20 for a
[tex]4 = 20 * b^{1.5[/tex]
Divide by 20
[tex]0.2 =b^{1.5[/tex]
[tex]b^{1.5} = 0.2[/tex]
Take 1.5th root of both sides
[tex]b = 0.34199518933[/tex]
[tex]b = 0.3[/tex] --- approximated
To the nearest degree, what is the mean (average) temperature of the data set below
23°, 17°, 26°, 5°, 33°, 11°
A. 19°
B. 20°
C. 26°
D. 28°
Answer:
A. 19°
Step-by-step explanation:
To find the average of something, you add every number in the sequence and then divide it by how many numbers there are.
23 + 17 + 26 + 5 + 33 + 11 = 115
115 / 6 = 19.16666666666667
Round it down and your answer will be 19°.
What number is in between 1.89 and 1.11
Answer:
Any number between 1.88-1.12
Step-by-step explanation:
1.88 or 1.12
for instance 1.9 , 1.92 ,1.93 1.94 ,1.95,1.96,1.97,1.98,1.99,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,1.91
There are infinite numbers because it is real number
log8(216)+[log(42)_log(6)]÷log(49)
Answer:
3 log (3) + 1/2Step-by-step explanation:
log8(216) + [log(42) - log(6)] ÷ log(49) =log (216)/ log (8) + [log (7) + log (6) - log (6)] ÷ 2 log (7) =3 log (3) log (2) / 3 log (2) + log (7) / 2 log (7) = 3 log (3) + 1/2select the three expressions that are equivalent to 3/5a + 10
A. 1/5a + 10 + 2/5a
B. a(3/5 + 10)
C. 14 + 3/5a - 4
D. 1/5 (3a + 50)
E. 10 + 2/5a - a + 1/5a
Answer:
A, C and D
Step-by-step explanation:
Given
[tex]\frac{3}{5}a + 10[/tex]
Required
Select 3 equivalent expressions
[tex]\frac{3}{5}a + 10[/tex]
Express 3 as 2 + 1
[tex]\frac{2 + 1}{5}a + 10[/tex]
Rewrite as:
[tex]\frac{2a + a}{5} + 10[/tex]
Split
[tex]\frac{2a}{5} + \frac{a}{5} + 10[/tex] ----- Option (A)
[tex]\frac{3}{5}a + 10[/tex]
Express 10 as 14 - 4
[tex]\frac{3}{5}a + 14 - 4[/tex]
Rewrite as:
[tex]14+\frac{3}{5}a - 4[/tex] --- Option (C)
[tex]\frac{3}{5}a + 10[/tex]
Factor out 1/5
[tex]\frac{1}{5}(3a + 50)[/tex] --- Option D
Answer:
Option D
Step-by-step explanation:
You can give the guy/girl above Brainliest ^^
They rlly went out of their way to answer that question for you.
They deserve it!
cost price of television is Rs 40000.The profit is 1/9 of selling price ,find the selling price .
Answer:
₹45000
Step-by-step explanation:
Let the selling price (SP) of the television be ₹x.
Therefore,
Profit [tex] =\frac{1}{9}x[/tex]
Cost price (CP) = ₹ 40000
[tex]Profit = SP - CP \\ \\ \frac{1}{9}x = x - 40000 \\ \\ \frac{x}{9} - x = - 40000 \\ \\ \frac{x - 9x}{9} = - 40000 \\ \\ - \frac{8}{9} x = - 40000 \\ \\ x = 40000 \times \frac{9}{8} \\ \\ x = 5000 \times 9 \\ \\ x = 45000[/tex]
WILL GIVE BRAINLIST BLS HELP Find z. Just write the number. Answer should be a whole number.
Answer:
I think the anwser is 8
Step-by-step explanation:
Answer:
It will be 8
Step-by-step explanation:
because the triangle will be in a ratio of 1:[tex]\sqrt{3}[/tex]:2, here 1 corresponds to 4, so the sides will be 4, 4\sqrt{3} and 8!
ITS AN EMERGENCY PLEASE HELP
Answer:
$9.80
Step-by-step explanation:
Remember that the way to find the mean of a data set is by adding together all the values, and dividing by the number of the values. So, in this case, you add the 5 values together and get 49. Since there are 5 values, you divide 49 by 5 and get 9.8, or in a real world-money situation $9.80.
The table shows the number of sodas left in the vending machine after each hour.
Time in Hours
0
1
2
3
Number of Sodas 310 290 270 250
If the pattern stays the same, which expression gives the number of sodas left after t hours?
A. 250 - 200
B. 290 - 200
C. 310 - 20t
D. 330 - 200
Answer: A
Step-by-step explanation: -20
what is the value of x?
Answer:
40
Step-by-step explanation:
135-95
im not 100% sure tho
1. x²+2xy+y²
2. x²-8x+16
3. 16a⁴_24a²b²+9b
Answer:
1.(x+y)²
2. (x-4)²
3. (4a²-3b²)²
What is the value of this expression? {18÷(2+4)}+3×2 Enter your answer in the box.
Answer:
The value of the expression is 78
Step-by-step explanation:
Answer:
Step-by-step explanation:
{18÷(2+4)}+3×2 = {18÷6}+3×2
= 3+3×2
= 3+6
= 9
Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it.
12(x + 3) = (y - 2)^2
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation.
(1 point)
b) What is the vertex of the parabola? (1 point)
c) What is the focus of the parabola? (2 points)
d) What is the directrix of the parabola? (2 points)
e) Sketch a graph of the parabola and label the vertex, focus, directrix, and axis of symmetry. (4 point
Answer:
a) The axis of symmetry is the line, y = 2
b) The vertex of a parabola is (-3, 2)
c) The focus of the parabola is (0, 2)
d) The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola
Step-by-step explanation:
a) The function for the parabola can be expressed as follows;
12·(x + 3) = (y - 2)²
The general form of the equation of the parabola is x = a·(y - k)² + h
The axis of symmetry is the line, y = k
By comparison, with the given equation of the parabola, we have;
12·(x + 3) = (y - 2)²
x = (1/12)·(y - 2)² - 3
Therefore;
a = (1/12), k = 2, h = -3
The axis of symmetry is y = k
∴ The axis of symmetry is the line, y = 2
b) The vertex of a parabola = (h, k)
∴ The vertex of a parabola = (-3, 2)
c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]
Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)
The focus of the parabola = (0, 2)
d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]
[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]
The directrix of a parabola is, x = -6
e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel
The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
It is given that the parabola equation is [tex]\rm 12(x+3)=(y-2)^2[/tex]
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We know the standard form of a parabola is:
[tex]\rm x= a(y-k)^2+h[/tex] .........(1)
We have the equation of parabola:
[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)
a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.
By comparing the equation (1) and (2), we get:
Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.
b) Vertex of the parabola = (h,k): (-3, 2)
c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],
[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]
∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]
The focus of the parabola is (0, 2)
d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]
[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]
The directrix of a is x = -6
e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry
Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6
Know more about the parabola here:
brainly.com/question/8708520
choose the correct equation please
Answer:
y=3×+6
Step-by-step explanation:
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A net of a three-dimensional figure is shown.
5 ft
4.ft
10 ft
6 ft
SED
What is the surface area of the three-dimensional figure?
Answer:
184 ft²
Step-by-step explanation:
16x10=160
2x1/2x4x6=24
160+24=184
A car travels 6 mile in 2 hours what is the unit rate
A 3 miles/ hour
B 1 mile/3 hour
C 3 /1 mile
D6 miles/ 1 hour
Answer:
A
Step-by-step explanation:
This is a fraction equal to
6 miles ÷ 2 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2
6 miles ÷ 2 2 hours ÷ 2= 3 miles1 hour= 3 miles hour = 3 miles per hour
Help me pls this is urgent ;>
Answer:
[tex] \frac{ |a + x| }{2} - \frac{ |a - x| }{2} \\ \\ = \frac{ | - 2 - 6| }{2} - \frac{ | - 2 + 6| }{2} \\ \\ = \frac{ | - 8| }{2} - \frac{ |4| }{2} \\ \\ = \frac{8}{2} - \frac{4}{2} \\ \\ = 4 - 2 = 2[/tex]
Find the surface area of the prism. A solid with six rectangular faces that has length 5 inches, width 3 inches, and height 7 inches. 5 in 3 in 7 in The surface area of the prism is ?
Answer:
290in
Step-by-step explanation:
Mrs. Stephens bought 3 pounds of tomatoes.How many ounces are equal to 3 pounds?
Answer:
48 ounces
Step-by-step explanation:
16 ounces per pound
3 x 16 = 48 ounces
Please help
For 20 points
Answer:
Step-by-step explanation:
Vertex: ( -2, -25)
Axis of symmetry: -2
I just need these 4, they should be super easy!! I really need help
Answer:
1. v = 72
2. b = 8
3. 0 or -2
4. C = -24
Step-by-step explanation:
Hope this helps.. Can I get brainiest