Using the z-distribution, as we are working with a proportion, it is found that the 83% confidence interval is (0.5789, 0.7611).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have an 83% confidence level, hence[tex]\alpha = 0.93[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.83}{2} = 0.915[/tex], so the critical value is z = 1.37.
The other parameters are [tex]n = 50, \pi = 0.67[/tex].
Then, the bounds of the interval are given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 - 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.5789[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.67 + 1.37\sqrt{\frac{0.67(0.33)}{50}} = 0.7611[/tex]
The 83% confidence interval is (0.5789, 0.7611).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Answer:
CI = (57.89%, 76.14%)
Step-by-step explanation:
First, solve for the 83% critical z-value (za/2). Second, solve for the margin of error. Third, solve for the confidence interval by subtracting and adding the margin of error with the sample probability of success.
If 0 is an angle in quadrant II, what is the value of cos0?
in the II Quadrant, let's recall that the adjacent side or cosine is negative whilst the opposite side or sine is positive, thus
[tex]tan(\theta )=-\sqrt{\cfrac{19}{17}}\implies tan(\theta )=\cfrac{\stackrel{opposite}{\sqrt{19}}}{\underset{adjacent}{-\sqrt{17}}}\impliedby \qquad \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]c=\sqrt{(-\sqrt{17})^2~~ + ~~(\sqrt{19})^2}\implies c=\sqrt{17+19}\implies c=\sqrt{36}\implies c=6 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{17}}}{\underset{hypotenuse}{6}}~\hfill[/tex]
Complete this proportion: 6/8 = a/12.
Answer:
9
Step-by-step explanation:
6 x
- = -
8 12
the relationship from 8 to 12 is divided by.666666666666
So, we do the same for 6
We get 9.
Find two positive consecutive
even integers such that the
square of the smaller integer
decreased by five times the
larger integer is 536.
Answer:
[tex]26[/tex] and [tex]28[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].
The square of the smaller integer would be [tex]x^{2}[/tex].
Five times the larger integer would be [tex]5\, (x + 2)[/tex].
Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].
The value of this expression should be equal to [tex]536[/tex]. In other words:
[tex]x^{2} - 5\, (x + 2) = 536[/tex].
Rewrite and simplify this quadratic equation:
[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].
[tex]a = 1[/tex].[tex]b = (-5)[/tex].[tex]c = (-546)[/tex]Apply the quadratic formula to find possible values of [tex]x[/tex]:
[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].
[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].
Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.
Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].
HELP ASAP 50 POINTS ITS GEOMENTRY
Answer:
1.c
2.a
3.d
4.e
5.f
6.b
find the area of the shape below
Answer:
396 cm²
Step-by-step explanation:
Let us break this shape into two parts.
The left part:
27 cm² * 10 cm² = 270 cm²
The right part:
24 cm² - 10 cm² = 14 cm²
14 cm² * 9 cm² = 126 cm²
Total area:
270 cm² + 126 cm² = 396 cm²
NEED HELP ASAP!!!!
Which equations define y as a linear function of x ?
Select all that apply.
A
y=2x
B
y=5x3+3
C
y=12x−9
D
y=x2
E
y=4x2+2x
F
y=2(4x−2)+16
Answer: A, C, F
Step-by-step explanation:
help this is due tom
Answer:
9. (a) 1/4
(b) remove 3 alphabet cards
(c) add 4 number cards
10. 1/8
Step-by-step explanation:
Question 9
Given:
8 number cards10 alphabet cards6 picture cards⇒ total number of cards = 8 + 10 + 6 = 24 cards
[tex]\mathsf{Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ outcomes}}[/tex]
(a) P(picture card) = 6/24 = 1/4
(b) P(alphabet card) = 10/24 = 5/12
If we remove 3 alphabet cards from the box
⇒ number of alphabet cards = 10 - 3 = 7
⇒ total number of cards = 24 - 3 = 21
Therefore, P(alphabet card) = 7/21 = 1/3
(c) P(number card) = 8/24 = 1/3
If we add 4 number cards to the box:
⇒ number of number cards = 8 + 4 = 12
⇒ total number of cards = 24 + 4 = 28
Therefore, P(number card) = 12/28 = 3/7
--------------------------------------------------------------------
Question 10
Given:
ΔSDR = ΔPRQLeg length of ΔSDR and ΔPRQ = 4 cm⇒ area of ΔSDR = area of ΔPRQ = 1/2 × 4 × 4 = 8 cm²
As PR = SD = 4cm
Area of rectangle = (4 + 4) × (12 + 4) = 128 cm²
P(point lies in ΔSDR) = 8/128 = 1/16
P(point lies in ΔPRQ) = 8/128 = 1/16
P(point lies in ΔSDR) OR P(point lies in ΔPRQ) = 1/16 + 1/16 = 2/16 = 1/8
(PLS HELP QUICK POINTS)
A soda can holds 235.5 in^3 of liquid. If the cab is 5 inches tall, what is the distance across the top of the soda can.
Answer:
Step-by-step explanation:
To make a guess as to the volume, it may be easier to guess in cups rather than centimeters or inches. One may visualize that a 12 ounce soda can is about 1.5 cups. This is equivalent to 354.88 cubic centimeters or 21.656 cubic inches.
find the total surface area of this triangular prism
answer quick
Answer:
716
Step-by-step explanation:
Triangle = bh / 2
24 x 14 = 336, you should divide by 2 but there is 2 of them (front and back) so cancels out. 10 x 24 is 240 and cancels for same reason. 336 + 240 = 576. 14 x 10 = 140 and 576 + 140 = 716
Answer:
976 cm^2
Step-by-step explanation:
area of triangle is 1/2 times base times height
notice we have two triangles
so 14 * 24 * 0.5 is 168
168 times 2 is 336
now we have a rectangle on the bottom so its area is base times height
14 times 10 is 140
and now we have two rectangles on either side
25 times 10 is 250
250 times 2 is 500
500+140+336
976 cm^2
HELP ASAP WILL GIVE BRAINLIEST!!!
Answer:
1222 ft^2
Step-by-step explanation:
2(13x9) + 2(5x12) + 2(4.5x9) + 2(9x11) + 2(19x11) + (19x9)
Pls Hurry.
What is the area of a rectangle with vertices (Negative 8, Negative 2), (Negative 3, Negative 2), (Negative 3, Negative 6), and (Negative 8, Negative 6)?
___ square units
Answer:
20units^2
Step-by-step explanation:
Answer:
20units^2
Step-by-step explanation:
Solve the system by substitution.
8x +y = 4
-23 – 8= y
Answer:
(2,-12)
Step-by-step explanation:
Correct equations:
8x+y=4
-2x-8=y
------------------
Rearrange the first equation:
8x+y=4
y=4-8x
Now use this value of y in the second equation:
-2x-8=y
-2x-8=4-8x
6x = 12
x = 2
When x = 2:
y=4-8x
y=4-8(2)
y = -12
(2,-12)
--
One can also graph the two equations and find the point they intersect. See the attached graph.
ILL GIVE BRAINIEST
I’ll give brainiest A marble has a radius of 2 cm. About how many marbles will it take to fill a cylindrical jar with a diameter of 16 cm and a height of 20 cm? (Volume of a sphere =
4
3
r
3
π
4
3
r
3
π
)
A.
40 marbles
B.
80 marbles
C.
120 marbles
D.
240 marbles
Answer:
120 marbles
Step-by-step explanation:
we can find the answer by dividing the volume of the cylinder by the volume of the marble.
V of a cylinder is
pi×r^2×h = 1280pi
V of marble is
4/3 × pi × r^3
V is 32/3 pi
so final answer is 1280pi ÷ (32/3 × pi)
ANSWER IS 120 MARBLES
a store is having a clearance special and every item is 20% off what is the sale price of a 230 suit
Answer:
184
Step-by-step explanation:
80% of 230
0.8x230
8×23
=184
28 is increased by 150%. what's the final number
Answer:
70
Step-by-step explanation:
20x(1+150%)
28x(1+1.5)
28x2.5
70
PLEASE HELP!!!!!!!!
How do I write these in Slope y-intercept form example: y=1/2x-5
7) 2x - y = 3
8) 2x+4y = 8
9) 3x-5y=10
10) 3x-1/2y=2
Answer:
The answers would be:
7) y=-0.5x+2
8) y=-0.5x+2
9) y=0.6x-2
10) y=6x-4
Step-by-step explanation:
An adult takes 400mg of vitamin c.
Each hour, the amount of vitamin c in
the person's system decreases by about
29%. How much vitamin c is left after 6
hours?
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
Which of the following graphs has a zero at (-5)?
A number cube with a number 1 through 6 is rolled. find the probability of rolling a number greater than 3?
The probability of rolling a number greater than 3 is equal to
--> # of numbers greater than 3 / total # of numbers on the dice
--> [tex]\frac{3}{6} =\frac{1}{2}[/tex]
There the probability of rolling a number greater than 3 is 1/2
Hope that helps!
help... Reference books are for use in the library. There are 16 bookshelves for the reference books. After use, they need to be returned to a special collection box for shelving. If 128 reference books are in use and 84 reference books are in the collection box, how many reference books are on the shelf?
Answer:
Your answer would be:
13.25
128 books in use + 84 books in the collection box =212 reference books on the shelf
212 books / 16 shelves =13.25 per shelf
Logically the answer 13.25 wouldn't make sense because you can't put a 25th of a book on a shelf, so that means you will need to put the "0.25 book" away. Technically your answer would be 13. Due to the question, however, it would be 13.25.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Match the following
A)
B)
C)
(Sorry if I didn’t put a picture it won’t let me do it…)
Answer:
No picture
Step-by-step explanation:
brain boggling boggle help pls
:)
Observe the division shown
To divide 2 by 9 Carl added a .0 on right of dividend and 0. on the right of quiotent .
Then he got 0.2Remainder recieved is 2 again
So these steps gonna repeating
The answer be like 0.222222..
16
21
Jade works as a decorator.
She is paid £22.80 per hour for the first 35 hours she works each week.
She is paid 15% more per hour for each extra hour she works.
One week, Jade was paid £981.54
In total, how many hours did she work that week?
You must show your working.
Let's assume that all hours she worked were the first 35 hours of the week.
She would've made £22.80 x 35 = £798
So, she would've made 981.54 - 798 = 183.54 less than the actual amount
She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.
So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours
So in total, she worked for 35 + 7 = 42(hours).
Answer:
42 hours
We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.
981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.
and 35 plus 7 = 42 :)
this morning carlos enters the room late. the distance from the road from their house to the school is 100 meters but he could travel it for 50 seconds what is his speed
Answer:
2 m/s or 7.2 km/h
Step-by-step explanation:
Time = 50 seconds
Distance = 100 meters
Velocity = distance/time = 100/50 = 2 m/s or 7.2 km/h
[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]
[tex] \large \purple{ \rm{Given↦}}[/tex]
Distance by road from their house to the school is 100 m.Time Given 50 sec[tex]\rule{70mm}{2.2pt}[/tex]
[tex] \large \purple{ \rm{To \: find↦}}[/tex]
Carlos speed[tex]\rule{70mm}{2.2pt}[/tex]
[tex] \large \purple { \rm{Assumption↦}}[/tex]
let the speed be x[tex]\rule{70mm}{2.2pt}[/tex]
[tex] \large \purple { \rm{ To \: find \: speed \: we \: use↦}}[/tex]
[tex] {\boxed{ \rm{Speed= \frac{ Distance } {Time}}}}[/tex]
[tex]\rule{70mm}{2.2pt}[/tex]
[tex] \large \purple{ \rm{Substitute \: value \: according \: to \: formula. \: }}[/tex]
[tex] \large \rm{s = \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = \cancel \frac{100}{50} }~~~~~~~~~~~~~~~~~~~~ \\ \\ \large \rm{s = 2 m/s \: or \: 7.2km/h }[/tex]
[tex]\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}[/tex]
[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
The difference of x and 7 is at most -28. Translate the sentence into an inequality
Answer:
x - 7 [tex]\leq[/tex] -28
Step-by-step explanation:
I guarantee you that this is correct. It's pretty simple to understand.
Please mark Brainliest. :)
Which number is irrational?
8√
0.8¯
0.46
100√3
Answer:
I think √8
Step-by-step explanation:
an integer to the power of 2
find the missing side length.
Use the formula shown:
6^2 + 2.5^ = c^2
36 + 6.25 = c^2
42.25 = c^2
Take the square root of both sides:
c = 13/2 as a fraction or 2.5495 as a decimal (round off as needed)
Find the area of the shaded polygon.
Answer:
A = 64 sq. unStep-by-step explanation:
This is a trapezium.
The formula od an area of a trapezium:
A = 1/2(a + b) · h
We have:
a = 10, b = 6, h = 8
substitute:
A = 1/2 · (10 + 6) · 8 = 1/2 · 16 · 8 = 8 · 8 = 64
Answer:
A = 64 sq. un
Step-by-step explanation:
6 * 8 + (4 * 8)/2 =
48 + 4 * 4 =
48 + 16 =
64
Solve and show your work for each question.
(a) What is expressed as a fraction in simplest form?
(b) What is expressed as a fraction in simplest form?
(c) What is expressed as a fraction in simplest form?
The value of 0.36 when converted to a fraction in the simplest form is 9/25.
How to calculate fractions in simplest form?Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.
From example, let's convert 0.36 to a fraction on its simplest form. This will be:
0.36 = 36/100 = 9/25
In conclusion, 0.36 is 9/25 in the simplest form.
Learn more about fractions on:
https://brainly.com/question/78672
Reflect the shape A in the line x=1
What are the coordinates of the vertices of the image?
Answer:
(0,4) (0,7) (-2,4)
Step-by-step explanation:
The line x=1 is a vertical line that passes through the point (1,0). So we then place the new triangle at equal distance from the line.
I hope this helps!
please mark brainliest!!
Answer:
i think you have to multiply
the answer is- 28.512
Step-by-step explanation:
i dont know if this is right im sorry but i think it is