Answer:
107 i think
Step-by-step explanation:
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. A sorority on campus wonders if their members have a different height, on average, from the population of American women. The mean height of group, which includes 25 members, is 65 inches.
A) Calculate the standard error for the distribution of means.
B) Calculate the z statistic for the sorority group.
C) What is the approximate percentile for this sample? Enter as a whole number.
D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?
Answer:
a) s = 0.4
b) Z = 2.5
c) 99th percentile.
d) The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.
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.
Assume the average height for American women is 64 inches with a standard deviation of 2 inches
This means that [tex]\mu = 64, \sigma = 2[/tex]
A) Calculate the standard error for the distribution of means.
Sample of 25 means that [tex]n = 25[/tex], so [tex]s = \frac{2}{\sqrt{25}} = 0.4[/tex].
B) Calculate the z statistic for the sorority group.
Sample mean of 65 means that [tex]X = 65[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{0.4}[/tex]
[tex]Z = \frac{65 - 64}{0.4}[/tex]
[tex]Z = 2.5[/tex]
C) What is the approximate percentile for this sample? Enter as a whole number.
Z = 2.5 has a p-value of 0.9938, so 0.99*100 = 99th percentile.
D) If the sorority actually had 36 members (still with an average of 65 inches), would you expect the percentile value to increase or decrease? why?
The larger sample size would lead to a smaller margin of error, which would lead to a higher z-score and a increased percentile.
The slope of the line graphed below is -3.
true or false?
Answer:
False, the slope is POSITIVE 3.
What is the solution to the equation below? Round your answer to two
decimal places.
ex = 7.9
The value of x will be 2.067.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ eˣ = 7.9
Now,
Since, The expression is,
⇒ eˣ = 7.9
Take natural log both side, we get;
⇒ ln eˣ = ln 7.9
⇒ x = ln 79 - ln 10
⇒ x = 4.369 - 2.302
⇒ x = 2.067
Thus, The value of x = 2.067
Learn more about the mathematical expression visit:
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Which values of c will allow the polynomial to be factored?
x² - cx - 24
Answer:
the possible values of c = -23, -10, -5, or -2
Step-by-step explanation:
The possible values of c that will allow the polynomial to be factored must be a factor of "-24"
1 x (-24) = -24 (for this case c = -23)
2 x (-12) = -24 (for this case c = -10)
3 x (-8) = -24 (for this case c = -5)
4 x (-6) = -24 (for this case c = -2)
Therefore, the possible values of c = -23, -10, -5, or -2
For his long distance phone service, Keith pays a $5 monthly fee plus 9 cents per minute. Last month, Keith's long distance bill was $21.02. For how many
minutes was Keith billed?
Answer: 178 minutes
21.02 x 100 = 2102
2102 - 500 = 1602
1602 / 9 = 178
What is the value of log↓3 81? 2, 3, 4 or 5?
Answer:The value of log base 3 log base 2 log base √3 81 is -a)1 b) 2 c)3 d) 0
Answer:
4
Step-by-step explanation:
Define [tex]\log_a b=c\implies a^c=b[/tex].
Let
[tex]\log_3 81=x[/tex].
Using our definition [tex]\log_a b=c\implies a^c=b[/tex], we have:
[tex]3^x=81[/tex]
Solving for [tex]x[/tex]:
[tex]x=\boxed{4}\text{ from simply knowing that }3^4=81[/tex]
Or
Algebraically solve step-by-step by taking the log of both sides:
[tex]\log 3^x=\log 81[/tex]
Using log property [tex]\log a^b=b\log a[/tex], rewrite:
[tex]x\log 3=\log81[/tex]
Divide both sides by log(3):
[tex]x=\frac{\log 81}{\log 3}=\boxed{4}[/tex]
Arianna has a coin collection. She keeps 4 of the coins in her box, which is 10% of the
collection. How many total coins are in her collection?
Answer: 40 coins. Doesn't your profile say college?
What choice is equivalent to the product below?
Answer:
Option C is the correct answer
[tex] {\frac{3 }{12}} [/tex]
Step-by-step explanation:
[tex]\huge \sqrt{\frac{3}{16}} . \sqrt{\frac{3}{9}} [/tex]
[tex] \huge =\sqrt{\frac{3\times 3}{16\times 9}} [/tex]
[tex]\huge =\sqrt{\frac{9}{144}} [/tex]
[tex] \huge =\sqrt{\frac{3^2 }{12^2 }} [/tex]
[tex]\huge ={\frac{3 }{12}} [/tex]
Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest or smallest possible values for the sum of X and Y.
9514 1404 393
Answer:
smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8
largest: 1x -9 = 8; 2y +3 = 7. total = 19
Step-by-step explanation:
If we use variables to represent the box contents, we can write ...
ax -b = cdy +e = fThen the values of x and y are ...
x = (c +b)/a
y = (f -e)/d
For positive integer values of the variables, x will always be positive, and y may or may not be negative.
Smallest sumFor the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.
x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for
8x -3 = 4 ⇒ x = 7/81y +9 = 2 ⇒ y = -7For these coefficients, the sum is -6 1/8 = -49/8.
(note that the values of 'b' and 'c' can be swapped with no net effect)
Largest sumFor the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for
1x -9 = 8 ⇒ x = 172y +3 = 7 ⇒ y = 2For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.
_____
Additional comment
These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.
Answer:
Smallest: 8x-3=4; 1y+9=2. total= -49/8
Largest: 1x-9=8; 2y+3= 7. total= 19
Step-by-step explanation:
#CARRYONLEARNINGIf f(x)=x^2 is vertically stretched by a factor of 9 to g(x). What is the equation of g(x)?
Given:
The function is:
[tex]f(x)=x^2[/tex]
This function is stretched by a factor of 9 to g(x).
To find:
The equation of function function g(x).
Solution:
The vertical stretch is defined as:
[tex]g(x)=kf(x)[/tex] ...(i)
If [tex]0<k<1[/tex], then the function f(x) compressed vertically by factor k.
If [tex]k>1[/tex], then the function f(x) stretched vertically by factor k.
The given function f(x) is stretched by a factor of 9 to g(x). So the value of k is 9.
Substituting [tex]k=9[/tex] in (i), we get
[tex]g(x)=9f(x)[/tex]
[tex]g(x)=9x^2[/tex] [tex][\because f(x)=x^2][/tex]
Therefore, the required function is [tex]g(x)=9x^2[/tex].
I’ll give brainliest
Answer:
d.18
Step-by-step explanation:
as x goes up by 1, y goes up 18
According to this diagram, what is sin 28°?
62
17
00
289
90°
15
A.
15
17.
B.
17
15
c.
17
D. 8
17
E. 15
8
Answer:
option d is correct
Step-by-step explanation:
taking 28 degree as reference angle . Then
sin 28 = opposite/hypotenuse
sin 28 = 8/17
The value of sin 28° is 8/17.
How to estimate the value of sin 28°?In the right triangle of the figure
Let, x be the opposite side angle of 28°
and y be the hypotenuse
[tex]$\sin \left(28^{\circ}\right)=\frac{x}{y}$[/tex]
We have,
x = 8 units and
y = 17 units
Substitute the values of x and y, we get
[tex]$\sin \left(28^{\circ}\right)=\frac{8}{17}$[/tex]
Therefore, the correct answer is option D. 8/17.
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Triangle ABC maps to triangle A′B′C′ by a 90∘ rotation counterclockwise about the origin.
If AB=61 units, BC=11 units, and AC=60 units, what is the length of A′C′?
60 units
11 units
90 units
61 units
Answer:
90
Step-by-step explanation:
One afternoon the water park sold 525 tickets for a total of $13,545. Child tickets cost $19 each, and adult tickets cost $40 each. How many of each kind of ticket were sold?
Answer:
c = 355 ; a = 170
Step-by-step explanation:
c = children
a = adults
c + a = 525
19c + 40a = 13545
19c + 19a = 9975
19c + 40a = 13545
-21a = - 3570
a = 170
c + 170 = 525
c = 355
help me I got 25 missing assignments
Answer:
think it's the last one
Step-by-step explanation:
sorry if i'm wrong
Consider the graph of g(x) = –2x2 + 8x – 10. Identify the y-intercept, the vertex, and the zeros of the function.
Question 10 options:
A)
y-intercept: (0, 10); vertex: (–2, 2); zeros: none
B)
y-intercept: (0, –10); vertex: (2, –2); zeros: (0,0) and (4,0)
C)
y-intercept: (0, –10); vertex: (2, –2); zeros: (0,0)
D)
y-intercept: (0, –10); vertex: (2, –2); zeros: none
9514 1404 393
Answer:
D) y-intercept: (0, -10); vertex: (2, -2); zeros: none
Step-by-step explanation:
The graph does not cross the x-axis, so there are no real zeros. It crosses the y-axis at (0, -10), so that is the y-intercept.
These observations match choice D.
What is mortgage of a 400000.00 loan at 6% 30 year fixed
9514 1404 393
Answer:
$2398.20
Step-by-step explanation:
Perhaps you want the monthly payment. It is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the principal amount, r is the annual interest rate, n is the number of payments per year, t is the number of years.
Your monthly payment will use P = 400,000; r = 0.06, n = 12, t = 30.
A = $400,000(0.06/12)/(1 -(1 +0.06/12)^(-12·30)) ≈ $2398.20
Is this correct? If not which is correct?
find the slope of the line between (1,4) and ( 3 , 10 )
Answer:
3
Step-by-step explanation:
slope of line = gradient of line
= [tex]\frac{10-4}{3-1}[/tex]
= 3
What is the completely factored form of this expression? 9x^3y - 100xy
Answer:
xy(3x+10)(3x-10)
4 in.
7 in.
O 124 6 in
87.9 in
O 97.5 in
O 78.9 in
5
6
7
Answer:
v=3.14 r 2 h
3.14 (2)(2)(7)= 87.9
Answer:
The answer for the Volume is 87.9 to 1d.p or 88in³ to the nearest tenth
Step-by-step explanation:
Volume of a cylinder =pir²h
r=d/2=4/2=2in
V=3.14×2²×7
V=3.14×4×7
V=87.92in³
V=87.9in³ to 1d.p
V=88in³ to the nearest tenth
max stores his paintbrushes in a box shaped like a rectangular prism. he can fill the bottom of the box with 48 one inch cubes. if the box is 4 inches tall,what is the volume
Answer:
192 inches^3 or 192 cubic inches
Step-by-step explanation:
48 one inch cubes means the base area is 48inches^2. 48inches^2 multiplied by 4 inches = 192inches^3
Answer: 192 square inches
Step-by-step explanation: it says that he can fill the bottom of the box with 48 once inch cubes, and since the cubes are an inch tall, the cubes would cover an inch of the box's height. The box's total height is 4, so you would need to multiply 4 by 48 to get the total number of cubes that can fit in the box, aka the volume of the box.
Aryav has 3,974 baseball cards. He wants to put them in collector sheets that hold 32 cards per sheet. How many sheets does Aryav need for his entire collection?
What can they do with the remainder?
Pls try to answer both questions.
Answer:
he will need 125 college tor sheets
3,974 / 32 =124.1875
I'm not sure about the second part its a little unclear.
Answer:
Step-by-step explanation:
3,974 / 32 = 124 R 6
I think they should give the remainder (6) away to other people or keep it and put it somewhere...
b. Why does using FOIL on polynomial expressions match so closely to integer
multiplication? Look closely at how the usual method works.
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport. What angle of depression does the airplane need to use to reach the runway?
Given :
An airplane flying at an altitude of 37,000 feet is still A horizontal distance of 100 miles (100 miles = 5280 ft) from the airport.
To Find :
What angle of depression does the airplane need to use to reach the runway?
Solution :
Let, angle of depression is [tex]\theta[/tex] .
So,
[tex]tan\ \theta = \dfrac{ Altitude \ in \ which \ plane \ is \ flying}{Horizontal \ Distance}\\\\tan \ \theta = \dfrac{37000}{5280}\\\\tan \ \theta = 7.00\\\\\theta = tan^{-1} 7\\\\\theta = 81.87^o[/tex]
Hence, this is the required solution.
Big math test I need help if I don’t I fail
How many different 4-digit PIN codes are there that only include the digits 5, 9, 6 and 2?
Answer:
256
Step-by-step explanation:
The digits can only be one of four numbers.
4*4*4*4 = 4^4 = 256
Here are five number cards.
2
5
7
8.
CO
One of the cards is removed and the mean average
of the remaining four number cards is 6
+
Which card was removed?
You must show your working.
+
Note: Please make sure your final answer says card ...
EC
brate Geb
Answer:
um I think that it could be 7 are 2
If point A, having
coordinates (p, 3) and
point B, with coordinates
(6, p) lie on a line having
a slope of 2, what is the
value of p?
gradient or slope=y2 -y1
x2 - x1
so for A, p is x1 and 3 is y1..
For B, 6 is x2 and p is y2
2= p - 3
6 - p
2 ( 6 - p) = p - 3
12 - 2p = p - 3
-2p + p = -3 - 12
-p = - 15
p = 15
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 23 f/s. The ball's height h (in feet) after t seconds is given by the following. Find all values of t for which the ball's height is 12 feet.
Answer:
Time taken = 0.85 and 0.59 (Approx.)
Step-by-step explanation:
Given:
Initial height = 4 feet
Initial upward velocity = 23 f/s
Equation;
h = 4 + 23t - 16t² for h = 12 feet
Find:
Time taken
Computation:
h = 4 + 23t - 16t² for h = 12 feet
12 = 4 + 23t - 16t²
16t² -23t + 8 = 0
t = [-b±√b²-4ac] / 2a
t = [23±√23²-(4)(16)(8)] / 2(16)
t = [23±√529-512] / 32
t = [23±4.12]/32
Time taken = 0.85 and 0.59 (Approx.)
