Answer:
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
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.
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17.
This means that [tex]\mu = 118, \sigma = 17[/tex]
A randomly selected group of 40 members
This means that [tex]n = 40, s = \frac{17}{\sqrt{40}} = 2.6879[/tex]
What is the probability of having a sample mean of 115.8 or less for a random sample of this size?
This is the pvalue of Z when X = 115.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115.8 - 118}{2.6879}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
Miya plans to visit her sister over the summer. On a map, her house is 2 inches from her sister’s house. If the map uses a scale of 1 inch = 18 miles, how many total actual miles would Miya travel on her trip to and back from her sister’s house?
HELP FAST HELP FAST THIS IS DUE
Answer:
72 miles
Step-by-step explanation:
18x2x2
need help with this please
Answer: plug 32 in for m
Step-by-step explanation:
if a+b=6 and ab=9 find the value of a3+b2
How to find the square root in long division method for 5.4289
(explanation attached)
will mark as brainliest
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros of -1, 2, and -3i. Show all work.
17 - (-25) =
I need help
Answer:
42
Step-by-step explanation:
rewrite by changing subtraction sign to addition and the following number to opposite
- always involves two sign changes
have a good day
need help with #10 please
Answer:
Domain = (infinity, infinity) Range = (3,0)
Step-by-step explanation:
Hard to explain without giving a 15 minute lecture lol
5. What number is in the ones place of a product of 10 and
another number? Explain.
A product of 10 has a number in one's position, and another figure will be 0.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The one number is 10.
And let the other number of two digits will be xy.
Then the product of 10 and another number will be
10 × xy = xy0
The number at ones place when the product of 10 and another number will be 0.
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Alicia is writing the program for a video game. For one part of the game she uses the rule (x,y) --> (x - 3, y + 4) to move points on the screen. ( Look at the picture to answer options A,B,C and show your work. If correct I'll Mark Brainliest.
Answer:
your answer is c
Step-by-step explanation:
Write the slope-intercept equation of the line passing through (4,6) and (0,-8).
Answer:
Answer:
[tex]y=\frac{7}{2} x -8[/tex]
Step-by-step explanation:
We are given that a line contains these 2 points: (4,6) and (0,-8), in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept
First, we need to find the slope of the line
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Even though we have 2 points, let's label their values to avoid any confusion and mistakes when calculating:
[tex]x_1=4\\y_1=6\\x_2=0\\y_2=-8[/tex]
Now substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-8-6}{0-4}[/tex]
Subtract
m=[tex]\frac{-14}{-4}[/tex]
Divide
m=[tex]\frac{7}{2}[/tex]
The slope is 7/2
Here is the equation of the line so far:
[tex]y=\frac{7}{2}x + b[/tex]
We now need to find b
As the equation passes through (4,6) and (0,-8), we can use either one of them to help solve for b.
Taking (4,6) for instance:
[tex]6=\frac{7}{2}(4) + b[/tex]
Multiply
[tex]6=14 + b[/tex]
Subtract
-8 = b
The equation therefore is:
[tex]y=\frac{7}{2} x -8[/tex]
Topic: slope-intercept form
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-3x-2=13
please show steps on how to do
Answer:
x=-5
Step-by-step explanation:
-5*-3=15
15-2=13
Hope it helps
Answer:
x = -5
Step-by-step explanation:
-3x-2=13
Add 2 to both sides of the equation
-3x-2+2=13+2
Simplify
-3x=15
Divide both sides of the equation by the same term
[tex]\frac{-3x}{3} =\frac{15}{-3}[/tex]
Simplify
x = -5
Shaniqua is taking a test. After 20 minutes she has 35 questions left. After 40 minutes she has 15 questions left. If Shaniqua takes the same amount of time for each question how many questions are on the test
There were 55 questions in the test.
Answer:
55
Step-by-step explanation:
A 26 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding down the wall at the instant of time when the bottom of the ladder is 10 ft from the wall and sliding away from the wall at the rate of 3 ft/sec?
Answer:
The top of the ladder is sliding down at a rate of -1.25 ft/s.
Step-by-step explanation:
From the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]
(Where a is the height, b is the distance between the bottom of the ladder and the wall, and c is the length of the ladder itself.)
Note that the hypotenuse c is a constant value at 26 feet. Substitute:
[tex]\displaystyle a^2 + b^2 = (26\text{ ft})^2 = 676 \text{ ft}^2[/tex]
We want to determine how fast the top of the ladder is sliding down the wall at the instant of time when the bottom of the ladder is 10 feet from the wall and sliding away from the wall at the rate of 3 ft/s.
In other words, we want to find da/dt given that b = 10 ft, and db/dt = 3 ft/s.
First, we can differentiate both sides with respect to t, where a and b are both functions of t:
[tex]\displaystyle \frac{d}{dt}\left[ a^2 + b^2\right ] = \frac{d}{dt}\left [ 676 \text{ feet}^2\right ][/tex]
Implicit differentiation yields:
[tex]\displaystyle 2a \frac{da}{dt} + 2b \frac{db}{dt} = 0[/tex]
Next, since we know that b = 10 ft, we can find a:
[tex]\displaystyle \begin{aligned} a^2 + b^2 & = 676\text{ ft}^2 \\ \\ a^2 +(10 \text{ ft})^2 & = 676\text{ ft}^2 \\ \\ a & = 24\text{ ft} \end{aligned}[/tex]
Substitute and solve for da/dt:
[tex]\displaystyle \begin{aligned} 2a \frac{da}{dt} + 2b\frac{db}{dt} & = 0 \\ \\ 2(24 \text{ ft}) \frac{da}{dt} + 2(10 \text{ ft})(3 \text{ ft/s}) & = 0 \\ \\ 48 \text{ ft} \cdot \frac{da}{dt} & = -60 \text{ ft$^2$/s} \\ \\ \frac{da}{dt} & = -1.25 \text{ ft/s} \end{aligned}[/tex]
Since the ladder is sliding down the wall, da/dt is expected to be negative.
In conclusion, the top of the ladder is sliding down at a rate of -1.25 ft/s.
PLEASE ANSWER ASAP‼
4-5c for C= -1/2
A principal of $2400 is invested at 7.25% Interest, compounded annually. How much will the investment be worth after 13 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
Step-by-step explanation:
70000
Solve 2 s^3 − 4r^ 2 if r = 1 and s = 5 . step by step
Answer:
246
Step-by-step explanation:
2(5)^3 - 4(1)^2
250 - 4
246
Write an equation of the line perpendicular to the given line that contains P.
P(5,-3); y=1/3x+4
Answer:
P(y,x)=P
y = 1/3x + 4
Step-by-step explanation:
Write 41 and 4 as a mixed number
Answer:
10 and 1 fourth
Step-by-step explanation:
41 over 4 = 41/4 so you divide 41 by 4 which is 10 R1 so its 10 wholes, 1 and 4
somone plz help me will make brainlest if is right
9514 1404 393
Answer:
y = 1/5
Step-by-step explanation:
Divide both sides of the equation by the coefficient of the variable.
7 = 35y
7/35 = (35y/35)
1/5 = 1y
y = 1/5
_____
A number divided by itself is 1. A number multiplied by 1 is unchanged.
To get from 35y to 1y, or y, divide by 35. That gives you (35/35)y = 1y = y.
Whatever you do to one side of the equation must also be done to the other side. Dividing 7 by 35 gives 7/35 = (7/7)×(1/5) = 1/5.
Determine what comes next in the given pattern 41,39,37,35,33
Answer:
31
Step-by-step explanation:
you're just subtracting by two's as the pattern goes on.
In the given pattern 41,39,37,35,33,the next number in the pattern is 31. To determine what comes next in the given pattern,let's observe the sequence:
41, 39, 37, 35, 33
The pattern is a decreasing sequence where each number is subtracted by 2 to get the next number.
So, to find the next number, subtract 2 from the last number in the sequence: 33 - 2 = 31
The next number in the pattern is 31.
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I will mark brainliest for the right answer with a description that helps me on how to actually solve this please
Answer:
$126
Step-by-step explanation:
I divided the figure in 3 parts, 1 triangle and 2 rectangles
found the area of each figure and added all to find the total area
Can someone please help me evaluate and show all your work please and thanks
Answer:
4
Step-by-step explanation:
-4/(k+7)
For k=-8
-4/(-8+7)
-4/-1
4
what number has the prime factorization 2 6th * 5 6th show your work
Find the area and perimeter.
5.6 cm
Answer:
31.36cm;22.4cm
Step-by-step explanation:
hope this helps
Answer:
Answer: 31.36 cm² ; 22.4 cm
Area:
[tex]{ \rm{area = (side \times side)}} \\ { \rm{area = (5.6 \times 5.6)}} \\{ \underline{ \underline { \rm{ \: \: area = 31.36 \: {cm}^{2} \: \: }}}}[/tex]
Perimeter:
[tex]{ \rm{perimeter = (4 \times side)}} \\ { \rm{perimeter = (4 \times 5.6)}} \\ { \underline{ \underline{ \rm{ \: \: perimeter = 22.4 \: cm \: \: }}}}[/tex]
Which of the following is an arithmetic sequence?
A. -2, -4, -8, -32...
B. 0, 5, 11, 24...
C. 1, -3, 9, -27, 81...
D. 0, 6, 12, 18, 24...
Answer:
The answer is letter D 0,6,12,18,24
Step-by-step explanation:
hope it's can help
WILL MARK BRAINLIEST Select the correct answer.
What is the slope of the line in this graph?
y 10
9
8
00
17
6
5
5
w
3
-2
N
X
1
2
3
5
ch
6
7
7
GO
9
10
ОА.
OB &
C.
9
OD
Hope this helps you !! :)
The solution is, the slope of the line in the graph is 5/7.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
from the given graph, we get,
the line is passing through the points ( 0,0) and, (5,7).
now, we know that
slope of a line is,
m = x1 - x2 / y1 - y2
so, we have,
here,
Slope(m) = 5-0/7-0
= 5/7
Hence, The solution is, the slope of the line in the graph is 5/7.
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The depth of water in a water tower that is draining is decreasing at a constant rate of 1.75 feet per hour. If
the depth after 6 hours of draining is 8 feet then write an equation for the water depth, d, as a function of the
amount of time it's been draining, t, in hours.
Answer:
1.75 * 6 = 10.5 - 8 = 2.5 / 1.75 = 1.43 * 5.5 = about 5hrs and 30mins
Step-by-step explanation:
*This problem is all about Multiplication Comparison*
How long is Pine Street?
Answer:
7
Step-by-step explanation:
Pine Street in x miles long.
Maple street is 3 times as long as Pine Street, so Maple street is 3x miles long.
Maple street is 21 miles long.
3x = 21
x = 7
Maple Street is 7 miles long.
pick
a
b
c
d .........................................................
Answer:
B
Step-by-step explanation:
Im pretty sure it's B X is going by 4's 4,8,12 then y is going by 12
A line is drawn so that it passes through the points (-5,0) and (12,7). What is the slope of the line?
Answer:
7/17
Step-by-step explanation: