A sample of n = 4 scores is selected from a normal population with μ = 30 and σ = 8. The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 2.00.
Answer:
False
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 establishes 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.
Population:
[tex]\mu = 30, \sigma = 8[/tex]
Sample of 4
This means that [tex]n = 4, s = \frac{8}{\sqrt{4}} = 4[/tex]
Probability of obtaining a sample mean greater than 34:
This is 1 subtracted by the p-value of Z when X = 34. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34 - 30}{4}[/tex]
[tex]Z = 1[/tex]
Thus, the probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z = 1.00, and the statement in this question is false.
Which of the following are exterior angles? Check all that apply.
A skateboarding ramp is 13in. high and rises at an angle of 13°. How long is the base of the ramp? Round to the nearest inch.
===========================================================
Explanation:
The diagram is shown below. We know the vertical part of the triangle is 13 inches, which is the side opposite the reference angle 13 degrees. The adjacent side is unknown. We'll call it x. This is how long the base of the ramp is, which is the horizontal distance along the entire ramp. This distance is on the ground. The ramp itself is the hypotenuse but it seems like your teacher isn't wanting to know this value. So we'll ignore the hypotenuse.
We'll use the tangent rule to connect the opposite and adjacent sides.
tan(angle) = opposite/adjacent
tan(13) = 13/x
x*tan(13) = 13
x = 13/tan(13)
x = 56.309186365694
x = 56 inches is the approximate horizontal distance underneath the ramp
The base of the ramp is 57 inches long.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The tangent function relates the opposite side (height) and adjacent side (base) of a right triangle to the angle of elevation.
We know the opposite side is the height of the ramp, which is 13 inches, and the angle of elevation is 13 degrees.
Let the adjacent side (the base of the ramp) be "x".
The tangent of 13 degrees is equal to the opposite side divided by the adjacent side:
tan(13) = 13/x
To solve for x, we can multiply both sides by x:
x × tan(13) = 13
Then, we can divide both sides by tan(13):
x = 13 / tan(13)
x = 13 / 0.228
x= 56.99
Therefore, the base of the ramp is 57 inches long.
To learn more on trigonometry click:
https://brainly.com/question/25122835
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What is 17.445 - 6.76 rounded to the nearest tenth
Answer:
10.7
Step-by-step explanation:
17.445 - 6.76= 10.685
10.685 is 10.7 when rounded to the nearest tenth!
Ms.Peralta's friend Mike is a construction worker. Mike gets paid $15 an hour. After working 9 hours he gets paid 1.25 times his hourly rate. Below you can find Mike's hours for last Friday. - Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - worked for an additional 7.5 hours How much money did Mike make last Friday?
Answer:
Mike made $ 200.63 last Friday.
Step-by-step explanation:
Since Ms. Peralta's friend Mike is a construction worker who gets paid $ 15 an hour, and after working 9 hours he gets paid 1.25 times his hourly rate, and last Friday Mike worked for 5 hours - took an 1 hr and 15 minute break for lunch (does not count toward his work hours) - and worked for an additional 7.5 hours, to determine how much money did Mike make last Friday the following calculation must be performed:
5 + 7.5 = 12.5
12.5 - 9 = 3.5
9 x 15 + (3.5 x (15 x 1.25)) = X
135 + 3.5 x 18.75 = X
135 + 65.625 = X
200.63 = X
Therefore, Mike made $ 200.63 last Friday.
Solve for 2. Round to the nearest tenth of a degree, if necessary.
L
90
K
80
J
Answer:
41.6
Step-by-step explanation:
got it wrong and it showed me the right answer
Help please, solve and explain
Answer:
Step-by-step explanation:
17.
18.
f(x)=6x^2+7x-4
(a)
f(3)=6(3)^2+7(3)-4
=54+21-4
=71
(b)
f(m)=6m^2+7m-4
(c)
f(x+1)=6(x+1)²+7(x+1)-4
=6(x²+2x+1)+7x+7-4
=12x²+12x+6+7x+7-4
=12x²+19x+9
19.
(fg)(x)=f(g(x)=f(2x²+3)=2x²+3+5=2x²+8
20.
(a)
f(x)=x²+3x+4
domain:all real values
(b)
domain:all real values≥-2
(c)f(x)=log(x+7)
Domain:x≥-7
21.
x²+6x+y²-7=0
(x²+6x+6/2)²)-(6/2)²+y²=7
(x+3)²+y²=7+9
(x+3)²+y²=4²
center=(-3,0)
radius=4
22.
(x-3)²+(y-5)²=3²
or
x²-6x+9+y²-10y+25=9
x²+y²-6x-10y+25=0
Graph is for 17th question.
Suppose that $2000 is invested at a rate of 4%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 5 years. Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Step-by-step explanation:
A = P(1+r/n)^ nt
A = 2000(1+.04/2)^(5*2)
A = [tex]2000(1.02)^{10}[/tex] = $2437.99
Please help me with this math
Answer:
(E) 9
Step-by-step explanation:
[tex]\frac{(3^{2008})^2-(3^{2006})^2}{(3^{2007})^2-(3^{2005})^2} = \\\frac{(3^{2007+1})^2-(3^{2007-1})^2}{(3^{2007})^2-(3^{2007-2})^2} = \\\frac{(3^{2007})^2(3^{2}-3^{-2} )}{(3^{2007})^2(1-3^{-4} )} =\\\frac{9-\frac{1}{9} }{1-\frac{1}{81} }=\\\frac{80}{9}:\frac{80}{81} = \\\frac{80}{9}*\frac{81}{80} = \frac{81}{9} = 9[/tex]
11. Juan earns $7 per hour at his job. Which ordered pair would not appear on a graph showing how much Juan
earns in x hours?
(3,21)
c. (5,35)
b. (4.14)
a.
d. (1,7)
Answer:
b. (4,14)
Step-by-step explanation:
Juan earns $7 per hour at his job.
This means that the ordered pairs showing his earnings y in x hours, (x,y), have the following format:
(x,7x).
Then, the ordered pairs are:
(1,7)
(2,14)
(3,21)
(4,28)
...
Thus, the ordered pair (4,14) would not appear on the graphic.
The measure of the angle of depression from the top of a 270-meter building to a park bench on the ground is 36°45′. How far away is the park bench from the building? Round to the nearest whole number.
Answer:
202 m
Step-by-step explanation:
Given :
Angle of depression, θ = 36°45' ; 45/60 = 0.75 = 36 + 0.75 = 36.75°
The height, h = 270
The distance of park bench from the building, d is given by :
Tan θ = opposite / Adjacent
Tan 36.75 = d / 270
d = 270 * Tan 36.75
d = 201.61856
d, distance of Park bench from building is 202 m
x^2+2x+7=21 the approximate value of the greatest solutoon to the equation, rounded to the nearest hundreth
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Answer:
x ≈ 2.87
Step-by-step explanation:
We can subtract 6 to put the equation into a form easily solved.
x^2 +2x +1 = 15
(x +1)^2 = 15
x +1 = √15 . . . . . for the greatest solution, we only need the positive root
x = √15 -1 ≈ 2.87
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answer: yes yes no yes yes no
Step-by-step explanation:
Can someone answer the question?
Answer:
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
Step-by-step explanation:
Division of complex numbers in polar form is [tex]z_1/z_2=\frac{r_1}{r_2}cis(\theta_1-\theta_2)[/tex] where [tex]z_1[/tex] and [tex]z_2[/tex] are the complex numbers being divided, [tex]r_1[/tex] and [tex]r_2[/tex] are the moduli, [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the arguments, and [tex]cis[/tex] is shorthand for [tex]cos\theta+isin\theta[/tex]. Therefore:
[tex]\frac{9(cos(\frac{11\pi}{6})+isin(\frac{11\pi}{6})) }{3\sqrt{3}((cos\frac{\pi}{4})+isin(\frac{\pi}{4})) }[/tex]
[tex]\frac{9}{3\sqrt{3} }cis(\frac{11\pi}{6}-\frac{\pi}{4})[/tex]
[tex]\frac{\sqrt{3} }{3} }cis(\frac{19\pi}{12})[/tex]
[tex]\frac{\sqrt{3} }{3} }(cos(\frac{19\pi}{12})+isin(\frac{19\pi}{12}))[/tex]
simplify my 5 multiply 6 - 60
Answer:
- 30 is the answer
Step-by-step explanation:
5 multiply 6 - 60
5 × 6 - 60
= 30 - 60
= - 30
Quantitative - Column chart
Quantitative - Line chart
Qualitative - Histogram
Qualitative - Pie chart
Answer:
A. Qualitative - Column chart
Step-by-step explanation:
Data could either be qualitative or quantitative. Quantitative data are usually given in a definite number, i.e it can be counted. While qualitative deals with characteristics, i.e it can be collected either by the use of questionnaires, or any similar method.
Therefore for the given question, the data survey is qualitative. And since the result would be presented as a graph showing the percentage users for each application, a column chart would be appropriate.
Thus for the data and its presentation, the answer is A. Quantitative - Column chart
Michelle is a financial analyst who works 47.75 hours a week. Michelle earns $27 per hour as a financial analyst, and her
overtime pay rate is time-and-a-half. If full-time employment is considered 40 hours per week, how much does Michelle
earn each week? Round to the nearest penny.
O $1,353.78
$1,393.88
$1,423,68
o $1.453.68
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Answer:
(b) $1,393.88
Step-by-step explanation:
For each overtime hour, Michelle is paid for 1.5 hours. That is we can figure her pay as though she worked straight time for ...
47.75 hours + (7.75 hours)/2 = 51.625 hours
That pay is ...
(51.625 h)($27/h) = $1393.88
1,4,1,8,1,16,1 what’s next in the sequence?
Answer:
32
hope this helps
have a good day :)
Step-by-step explanation:
Noah is carrying a bag that weighs 2.5 pounds. What is the weight of the bag equal to?
A. 30 oz.
B. 40 oz.
C. 50 oz.
D. 60 oz.
Answer:
B. 40 oz.
Step-by-step explanation:
I’ll mark you as brainliest
Step-by-step explanation:
1) 6s^2
(s mean the length of each side, s=7)
= 6x7^2
= 294
2) 2(3)(2)+2(1)(2)+2(3)(1)
（l=length, w=wide, h=height)
= 12+4+6
= 22
3) 4(π)12^2
(r=radius)
= 576
what is the equation that matches this table?
Answer:
y = –1 + 3x
Step-by-step explanation:
To know which option is correct, we shall use the equation given in each option to see which will validate the table. This is illustrated below:
Option 1
y = –1x + 3
x = –2
y = –1(–2) + 3
y = 2 + 3
y = 5
This did not give the required value of y (i.e –7) in the table.
Option 2
y = 1 + 3x
x = –2
y = 1 + 3(–2)
y = 1 – 6
y = –5
This did not give the required value of y (i.e –7) in the table.
Option 3
y = –3 + 1x
x = –2
y = –3 + 1(–2)
y = –3 – 2
y = –5
This did not give the required value of y (i.e –7) in the table.
Option 4
y = –1 + 3x
x = –2
y = –1 + 3(–2)
y = –1 – 6
y = –7
This gives the required value of y (i.e –7) in the table.
Thus, the equation that matches the table is:
y = –1 + 3x
Given that P(x) = 2W/W+1 + W-4/2W-3 , evaluate p(0)
Answer:
5
Step-by-step explanation:
jnjknmnj
Get brainiest if right!!
Mark has 1.5 times more collectible cards than Jacob. If Mark
gives Jacob 11 cards, they will have the same number of
collectible cards. How many cards do they have?
Answer:
17.5 cards
Step-by-step explanation:
11 x 1.5 = 16.5
16.5 + 11 = 17.5 cards
Answer:
110
Step-by-step explanation:
Let us take Jack cards as x
Then Mark cards will be 1.5 * x
Mark gives 11 cards to Jack...the equation is
1.5 * x - 11 = x + 11
Adding +11 on both sides
1.5*x -11 + 11 = x + 11 + 11
1.5*x = x + 22
Subtracting x on both sides
1.5*x - x = x + 22 - x
.5*x = 22
x = 22 * 1/.5 = 220/5 = 44
Now go back to the initial equation
Mark >> 1.5 * x = 66
Jack >> 1 * x = 44
Total >> 110.
PLS HELP IM BEING TIMEDWhich of these statements is true? A) 349 > 456 B) 456 < 792 792 < 456 D) 792 > 863
Answer:
B
Step-by-step explanation:
792 is a bigger number than 456
Answer: B
Step-by-step explanation: 792 is larger than 456
how much does a customer save for buying a sound system marked $1,200 at a discount of 15%
Answer:
Step-by-step explanation:
Mp=$1200
Let sp be x
SP=MP-discount% of MP
x=1200-15/100 * 1200
x=120000-18000/100
x=102000/100
x=1020
the amount of money person saves=MP-SP
=$1200-$1020
=$180
therefore he saves $180
In Triangle QRS, Angle R is a right angle, m angle Q = 57° and QS = 35. Which of the following expressions correctly
calculates the length of line QR ?
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Answer:
(3) 35·cos(57°)
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
For the given triangle, this is ...
cos(57°) = QR/QS
Multiplying by QS gives ...
QS·cos(57°) = QR
Filling in the value of QS, we have ...
QR = 35·cos(57°)
In ΔFGH, the measure of ∠H=90°, FH = 8, OF = 17, and HG = 15. What ratio represents the sine of ∠G?
Answer:
[tex]\sin(G) = \frac{8}{17}[/tex]
Step-by-step explanation:
Given
[tex]\angle H = 90^o[/tex]
[tex]FH = 8[/tex]
[tex]GF = 17[/tex]
[tex]HG = 15[/tex]
See attachment for illustration
Required
The ratio of [tex]\sin(G)[/tex]
[tex]\sin(G)[/tex] is calculated as:
[tex]\sin(G) = \frac{Opposite}{Hypotenuse}[/tex]
From the attachment, we have:
[tex]\sin(G) = \frac{FH}{GF}[/tex]
This gives:
[tex]\sin(G) = \frac{8}{17}[/tex]
10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1
Compare to the divergent series,
[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]
Then by the limit comparison test, the given series also diverges, since the limit
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]
is positive and finite.
calculate to the nearest million m³.the current amount of water in the berg river dam
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the dimension of the dam is not given.
However, a general way of calculating volume is to calculate the base area and the multiply by height.
Take for instance,the dam has a rectangular base of 20m by 30m.
The base area will be
Area = 20m * 30m = 600m²
If the height of the water in the dam is 40m, then the volume is:
Volume = 600m² * 40m
Volume = 24000m³
In 2009, a diabetic express company charged $38.85 for a vial of type A insulin and $30.34 for a vial of type B insulin. If a total of $1695.71 was collected for 50 vials of insulin, how many vials of each type were sold?
The number of vials of type A insulin sold were ___ and the number of vials of type B insulin sold were ____
Answer:
The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.
Step-by-step explanation:
Let a = number of type A vials.
Let b = number of type B vials.
38.85a + 30.34b = 1695.71
a + b = 50
38.85a + 30.34b = 1695.71
(+) -38.85a - 38.85b = -1942.50
---------------------------------------------------
-8.51b = -246.79
b = 29
a + b = 50
a + 29 = 50
a = 21
Answer: The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.
