Answer:
0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
37% of the company's orders come from first-time customers.
This means that [tex]p = 0.37[/tex]
A random sample of 225 orders will be used to estimate the proportion of first-time-customers.
This means that [tex]n = 225[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.37[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322[/tex]
What is the probability that the sample proportion is between 0.26 and 0.38?
This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.
X = 0.38
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.38 - 0.37}{0.0322}[/tex]
[tex]Z = 0.31[/tex]
[tex]Z = 0.31[/tex] has a pvalue of 0.6217
X = 0.26
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.26 - 0.37}{0.0322}[/tex]
[tex]Z = -3.42[/tex]
[tex]Z = -3.42[/tex] has a pvalue of 0.0003
0.6217 - 0.0003 = 0.6214
0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38
Please answer ASAP this is due tomorrow
Answer:
227.08in^2
You want to find the surface area for this problem. SA=2lw+2lh+2hw
Step-by-step explanation:
L=2.5
W=7.4
H=9.6
SA=2lw+2lh+2hw
SA=2(2.5x7.4)+2(2.5x9.6)+2(9.6x7.4)
SA=37+142.08+48
SA=227.08in^2
During science class, groups measure out different volumes of vinegar. The line plot below shows the amount of vinegar used by 12 groups, rounded to the nearest 1/2 ml.
Answer: it should be 22 1/2 :)
An element with
mass 510 grams decays by 26.3% per minute. How much of the
element is remaining after 7 minutes, to the nearest 10th of a gram?
Answer:
60.2 grams is remaining after 7 minutes.
Step-by-step explanation:
Exponential equation for amount of substance:
The exponential equation for the amount of a substance is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal, and t is the time measure.
An element with mass 510 grams decays by 26.3% per minute.
This means that [tex]A(0) = 510, r = 0.263[/tex]
So
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 510(1-0.263)^t[/tex]
[tex]A(t) = 510(0.737)^t[/tex]
How much of the element is remaining after 7 minutes?
This is A(7). So
[tex]A(7) = 510(0.737)^7 = 60.2[/tex]
60.2 grams is remaining after 7 minutes.
please help me understand and solve this
Step-by-step explanation:
just multiple them and you'll get the results and the results you got add them together
A park has a triangular sandbox. Todd wants to create a smaller sandbox at his backyard having the same angles as the park sandbox.
What is the perimeter in feet of Todd’s sandbox?
You purchase a car for $20,000. It depreciates 30% each year. Which formula calculates how much your car will be worth in 10 years?
Answer:6722.8(sorry if i'm wrong)
Step-by-step explanation:
Determine whether the following functions with their specified domain and range is injective, surjective, and bijective. If you determine that a given function with its specified domain and range is injective, surjective, or bijective, you do not need to prove it. On the other hand, if you determine that a given function with its specified domain and range fails to be injective, surjective, or bijective, you MUST provide a counter example.
a. f: R → R defined by f(x) = x^4 + 1.
b. f: R (1,0) defined by f(x) = x^4 + 1
c. f: R + R defined by f(x) = 2^x.
d. f: R (1,0) defined by f(x) = 2^x + 1.
Answer:
Step-by-step explanation:
[tex]\text{Given that:}[/tex]
[tex]f: \mathbb{R} \to \mathbb{R}[/tex] [tex]\text{which is de-fined by : } f(x) = x^4 + 1[/tex]
[tex]\mathbf{f \ is \ not \ injective}[/tex]
[tex]\mathtt{counterexample:}[/tex]
[tex]Assume \ x =1, y = -1 \\ \\ f(x) = 1^4 + 1= 2 \\ \\ f(y) = (-1)^4 + 1 = 2[/tex]
[tex]Hence \ f(x) = f(y) , but \ x \ne y[/tex]
[tex]Also;[/tex] [tex]f[/tex] [tex]\text{ is not surjective.}[/tex]
[tex]Take (y )= -10 \ \varepsilon \ \mathbb{R}[/tex]
[tex]\text{But there is no pre-image x such that}[/tex] [tex]f(x) = y[/tex]
[tex](b)[/tex]
[tex]f: \mathbb{R} \to (1, \infty) \ \ \text{which is de-fined as} \ f(x) = x^4 + 1 \\ \\ \text{f is injective and surjective and; thus bijective}[/tex]
[tex](c) \\ \\ f : \mathbb{R} \to \ \mathbb{R} \text{which can be de-fined as} \ f(x) = 2^x \\ \\ \text{f is injective and f is no surjective} \\ \\ \mathtt{counterexample:} \\ \\ Assume \ 2 \ \varepsilon \ \mathbb{R} \\ \\ whereas; 2^x = -2 \\ \text{which implies that }: \implies x = \dfrac{log_x(-2)}{log 2} = not \ de'fined[/tex]
[tex](d) f : \mathbb{R} \to (1 , \infty) , \ \text{which is de'fined by} \ \ f(x) = 2^x+1 \\ \\ \text{Thus; f is injective, surjective, and bijective}[/tex]
4 1/6 divided by 1 1/8
Answer:
3.7037037037
Step-by-step explanation:
Answer:
5 35/48
Step-by-step explanation:
25/6x11/8=275/48=5 35/48
9. square
A =
s= 15 ft
Answer:
225 square feet
Step-by-step explanation:
If one side = 15 ft, and it's a square, you do 15 x 15 = 225 square feet
Hope that helps!
Which inequality is graphed?
{Please Look at the Image , Then Summit Your answer}
Answer:
Its the last one because the sign is pointing to the right (x) and it has a line underneath, which would be a closed dot so therefore, the last one is the amswer
Step-by-step explanation:
Answer:
2 ∠ x
Step-by-step explanation:
The graph is going right of 2 which means x is greater than 2.
Quadrilateral KLMN is dilated by a scale factor of 2/3 to form quadrilateral K'L'M'N'. What is the measure of side NK?
Answer:
NK = 42
Step-by-step explanation:
Scale factor of dilating KLMN to form K'L'M'N' = ⅔. This fraction implies there was a reduction of the original shape to form the new image/shape.
NK corresponds to N'K'
N'K' = 28
To get the NK, divide 28 by the scale factor.
28 ÷ ⅔ = 28*³/2 = 42
NK = 42
Which of the following trigonometric ratios are correct?
9514 1404 393
Answer:
D, F
Step-by-step explanation:
The mnemonic SOH CAH TOA can help you with this. It reminds you ...
Sin = Opposite/Hypotenus
sin(40°) = x/b . . . . matches D
Cos = Adjacent/Hypotenuse
cos(40°) = a/b . . . . no match
Tan = Opposite/Adjacent
tan(40°) = x/a . . . . matches F
On a later day, he asked the same group of 10 friends to throw a ball again and collected another set of data. The median of the second data set is 49 feet, and the IQR is 6 feet.
a. Did the 10 friends, as a group, perform better (or throw farther) in the second round compared to the first round?
(Worse or better)
b. Were the distances in the second data set more variable or less variable compared to those in the first round?
(More variable or less variable)
Answer:
a
Step-by-step explanation:
how to solve 46 divide by 6 and change it to a multiplication equation
Answer:
46/6 is approximately 7.667.
To change it to a multiplication problem, I can do 46 = 6*7.667. The answer is not exact, just an estimated approximation.
You can also try to divide yourself.
What is the value of the digit 2 in the number 425,611?
Answer:
20,000 or 10,000
Step-by-step explanation:
The 2 is in the ten thousandth place, but the value is 20,000
OMG PLEASE HELP PLEASE OMG HELP ME HELP PLZ!!!!!!!!!! HELPPPPPPPPPPPPp
17.5 mark brainlist plssssssssssssss
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 18)(0,18) and (2, 1152)(2,1152).
Answer:
Step-by-step explanation:
let y=ab^x
x=0,y=18
18=ab^0=a
a=18
y=18b^x
when x=2,y=1152
[tex]1152=18b^{2}\\b^{2}=\frac{1152}{18}=64=8^2\\b=8\\so~y=18(8)^x[/tex]
A plane flies 545 kilometers with a bearing of 316° from Naples to Elgin (see figure). The plane then flies 680 kilometers from Elgin to Canton (Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton. (Round to the nearest whole number.)
Answer:
235°Step-by-step explanation:
Use of low of sinesConsider triangle CENBearing of angle counted from zero to the vector of flightWe have
∠CNE = complementary with 44° ⇒ m∠CNE = 90° - 44° = 46°NE = b = 545 kmEC = a = 680 km∠ECN = xFind the measure of angle x:
sin 46° / a = sin x / bsin 46° / 680 = sin x / 545sin x = 545 sin 46 deg / 680x = arcsin (545 sin 46 deg / 680)x = 35° (rounded)Bearing of the flight from Elgin to Canton is:
270° - 35° = 235° as the vector is in the third quadrantAnswer:
235°
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
The given scenario can be modeled as a triangle.
Given sides of the triangle:
a = 680 kmb = 545 kmAs due north is at a right angle to due west, the angle in the right corner of the triangle is:
⇒ 90° - 44° = 46°
Use the Sine Rule to find angle y marked on the attached diagram (the angle opposite side b).
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{\sin 46^{\circ}}{680}=\dfrac{\sin y}{545}[/tex]
[tex]\implies \sf \sin y= \dfrac{545\sin 46^{\circ}}{680}[/tex]
[tex]\implies \sf y= \sin^{-1} \left(\dfrac{545\sin 46^{\circ}}{680}\right)[/tex]
[tex]\implies \sf y=35.20682806...^{\circ}[/tex]
Interior angles of a triangle sum to 180°
⇒ x° + y° + 46° = 180°
⇒ x° + 35.2068...° + 46° = 180°
⇒ x° = 98.79317194...°
Consecutive Interior Angles Theorem
When a straight line intersects two parallel straight lines, the consecutive interior angles formed sum to 180°. Therefore the angle between due north and side a of the triangle is:
⇒ 180° - 44° = 136°
To find the bearing of the flight from Elgin to Canton, find the angle labelled green on the attached diagram:
[tex]\implies \sf Bearing =136^{\circ}+ 98.79317194...^{\circ}[/tex]
[tex]\implies \sf Bearing = 234.7931719...^{\circ}[/tex]
[tex]\implies \sf Bearing = 235^{\circ}[/tex]
As bearings are usually given as a three-figure bearings, the bearing of the flight from Elgin to Canton is 235°.
Learn more about bearings here:
https://brainly.com/question/27928951
The question that is asked...
<5 is a complement of <6 and m<5 = 59 degrees. Find m<6.
A pair of complementary angles, when added, equal 90. So if <5 is 59 degrees, what do you do to find <6? You subtract 59 with 90.
90-59=31
So <6 is 31 degrees.
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hope it helps
I will give 40 points to the person who has the awnser and work solved to all 5 questions
Answer:
4w+6h-h
4w+5h
7y+4y
11y
6x+3y+5x
11x+3y
5x+12d-2x+4d
3x+16d
3x^2+6y+5x^2+2x
8x^2+6y+2x
Let me know if this helps!
Answer:
A, D,and E
Step-by-step explanation:
Condense the log equation: 4 log x + log y - 5 log z
Answer:
The condensed log equation is: [tex]\log{\frac{x^4y}{z^5}}[/tex]
Step-by-step explanation:
We use these following logarithm properties to solve this question:
[tex]a\log{x} = \log{x^a}[/tex]
[tex]\log{a} + \log{b} = \log{ab}[/tex]
[tex]\log{a} - \log{b} = \log{\frac{a}{b}}[/tex]
In this question:
[tex]4\log{x} = \log{x^4}[/tex]
[tex]5\log{5} = \log{z^5}[/tex]
So
[tex]4\log{x} + \log{y} - 5\log{z}[/tex]
Becomes:
[tex]\log{x^4} + \log{y} - \log{z^5}[/tex]
Now applying the addition and subtraction properties, we have:
[tex]\log{\frac{x^4y}{z^5}}[/tex]
The condensed log equation is: [tex]\log{\frac{x^4y}{z^5}}[/tex]
Question 2(Multiple Choice Worth 1 points) (07.03 MC) Lacey has $36 to spend. She buys a pair of sunglasses for $14.89 and a hat for $9.33. Lacey buys a scarf with the remaining money. How much does Lacey spend buying a scarf? $4.66 $7.44 $11.78 $24.22
Answer:
11.78
Step-by-step explanation:
The question that is asked
Answer:
THE ANSWER IS B BECAUSE I AM BIG BRAIN
Step-by-step explanation:
I don't understand this, please help
Answer:
∠2 = 150°, it is a supplementary angle to 30°
∠3 = 30°, it is an alternate angle to 30°
∠4 = 150°, it is a supplementary angle to 30°
∠5 = 30°, it is an alternate angle to 30°
∠6 = 150°, it is a supplementary angle to 30°
∠7 = 30°, it is an alternate angle to 30°
∠8 = 150°, it is a supplementary angle to 30°
Please guys help me please no links
Answer:
it's F.
Step-by-step explanation:
i used my calculator. just trust me
3.1 Simplify the following ratios:
3.1.1 500g: 3 kg
- 15
Answer:
1g:6g-15
Step-by-step explanation:
Which of the following choices lists the values of the side longths of a triangle with 45-45-90 degree angles and a hypotonuso - 247? Need help
Answer:
D 12rad2 12rad2 24
Step-by-step explanation:
The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for Oregon residents. These data are based on simple random samples of 11,545 California and 4,691 Oregon residents.
(a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states.
(b) It is possible the conclusion of the test in part (a) is incorrect. If this is the case, what type of error was made?
Step-by-step explanation:
We start by stating the null hypothesis
H0: p1 = p2
No difference is existent
H1: p2 not equal to p2
There is a difference
We find the z statistic using microsoft excel or using the formula in the attachment
= -1.68
From the normal table, p value = 0.099
The p value is greater than 0.05 so we fail to reject the null hypothesis and conclude there is no difference
B. If answer in part a is incorrect then we have made a type ii error. A type 2 error occurs when we accept a false null hypothesis.
I need help on the griding for (1/2,2). Please explain. :(