Answer:
0.1836 = 18.36% probability that the sample mean would differ from the population mean by greater than 1.46 WPM
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.
The mean number of words per minute (WPM) read by sixth graders is 84 with a standard deviation of 15 WPM.
This means that [tex]\mu = 84, \sigma = 15[/tex]
Sample of 188
This means that [tex]n = 188, s = \frac{15}{\sqrt{188}}[/tex]
What is the probability that the sample mean would differ from the population mean by greater than 1.46 WPM?
Greater than 84 + 1.46 = 85.46 or less than 84 - 1.46 = 82.54. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Probability is is less than 82.54.
P-value of Z when X = 82.54. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{82.54 - 84}{\frac{15}{\sqrt{188}}}[/tex]
[tex]Z = -1.33[/tex]
[tex]Z = -1.33[/tex] has a p-value of 0.0918
2*0.0918 = 0.1836
0.1836 = 18.36% probability that the sample mean would differ from the population mean by greater than 1.46 WPM
PLEASE HELP ME!!
Two sides of a right triangle are 8 and 12 in.
a. Find the missing side if these are the lengths of the legs.
b. Find the missing side if these are the lengths of a leg and hypotenuse.
who has guathmath here. this is the invitation code. https://s.tutorus.xyz/lp/invite?code=F47XR9
Step-by-step explanation:
thank youjjdjdkdkdkdkkdididososiid
The answer I put is wrong. SO don't put that as a answer. NEED TO EXPLAIN VERY IMPORTANT
Brainleist
Answer:
Solution given:
Annie needs 250 lb of cement to fix the outer step.
Each bag hold 40 lb of cement.
Now
40 lb =1bag
we need
250lb= ? bag.
we have
no of bag =needed lb/1 bag's lb=250/40=250/40=6.25
we do not need more than 7 bags
Annie needs 7 bags.
So
The required inequality is:
b≥7.
Please help will mark BRAINLIEST!
=====================================================
Explanation:
We have n = 5 sides. This means the interior angles sum up to...
S = 180(n-2)
S = 180(5-2)
S = 180(3)
S = 540
All five interior angles of this pentagon add up to 540 degrees.
How do you solve this? Thanks.
Answer:
Simulateneous equation
Step-by-step explanation:
Have to slove the equation given then plot the graph
Answer:
Graph a line segment with endpoints (1,-8) and (-4,3).
Step-by-step explanation:
Just identity the endpoints of the line segment given, then swap the coordinates for each pair to graph it's inverse.
Original point -> Corresponding inverse point
(a,b) ->(b,a)
(-8,1) ->(1,-8)
(3,-4) ->(-4,3)
So graph the other inverse which is also a line segment using endpoints (1,-8) and (-4,3).
(The inverse graph is just a reflection of the original relation over y=x.)
Element X is a radioactive isotope such that every 25 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 910 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that [tex]A(0) = 910[/tex]
So
[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]
[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]
How long would it be until the mass of the sample reached 400 grams?
This is t for which [tex]A(t) = 400[/tex]
So
[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]
[tex]400 = 910(0.5)^{\frac{t}{25}}[/tex]
[tex](0.5)^{\frac{t}{25}} = \frac{400}{910}[/tex]
[tex](0.5)^{\frac{t}{25}} = 0.43956[/tex]
[tex]\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}[/tex]
[tex]\frac{t}{25}\log{0.5} = \log{0.43956}[/tex]
[tex]t = \frac{25\log{0.43956}}{\log{0.5}}[/tex]
[tex]t = 25.6[/tex]
It will take 25.6 years for the mass of the sample to reach 400 grams.
Answer:
29.6
Step-by-step explanation:
Ahmir is 20 years older than Brynn. In 5 years Ahmir will be 3 times as old as Brynn. What are their current ages?
Ahmir is 20, Brynn is 5.
Ahmir is 60, Brynn is 40.
Ahmir is 25, Brynn is 5.
Ahmir is 5, Brynn is 25.
Candace invests $636 in an investment that pays 7% interest compounded quarterly. What is her annual effective yield? Input answer as a percentage to two decimal places.
Answer:
7.19%
Step-by-step explanation:
let i be the effective rate
[tex](1+\frac{.07}{4})^4=(1+i)\\.071859031[/tex]
The annual effective yield will be 7.19% for the investment.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Given that Candace invests $636 in an investment that pays 7% interest compounded quarterly.
The annual effective yield will be calculated as below:-
[ ( 1 + ( 0.07 / 4 )⁴ ] = ( 1 + i)
Solve the equation:-
i = 0.0718
i = 0.0718 x 100 = 7.19%
Therefore, the annual effective yield will be 7.19% for the investment.
To know more about compound interest follow
https://brainly.com/question/24924853
#SPJ2
Given the Graph, identify the slope
Answer: The slope is -5/3 or -1.4
Algebra
[tex]s = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]s = \frac{5}{3} [/tex]
Help me please I need help 2
Answer:
26.6 meters
Step-by-step explanation:
Tan(x) = [tex]\frac{opp}{adj}[/tex]
Tan(28) = [tex]\frac{x}{50}[/tex]
x = 26.6m
What is the length of line segment CD?
Enter your answer, as a decimal rounded to the nearest tenth, in the box.
CD =
units
A graph with lines drawn between points A begin ordered pair 1, 3 end ordered pair and B begin ordered pair 4, 3 end ordered pair, points C begin ordered pair -2, 2 end ordered pair and D begin ordered pair 4, -4 end ordered pair, and points E begin ordered pair -7, 0 end ordered pair and F begin ordered pair -2, 4 end ordered pair
Answer:
Assume you need to find distance CD, between points C(-2, 2), D(4, -4)
Use distance formula:
[tex]CD = \sqrt{(4 + 2)^2+(-4-2)^2} = \sqrt{72} = 6\sqrt{2}[/tex] ≈ 8.5 unitsAnswer:
C(x1,y1)=(-2, 2), D(4, -4)
D(x2,y2)=(4, -4)
we have
the length of line segment CD
=[tex]\sqrt{(x2-x1)²+(y2-y1)²}\\ \sqrt{(4+2)²+(-4-2)²}=8.48 units[/tex]
Tom saves $750 a year. Bill saves $60 a month. How much more does Tom save a year than Bill?
Answer:
$30
Step-by-step explanation:
T = 750
B = 60(12)
T - B = X
750 - 720 = 30
Answer:
Tom saves 30 more dollars
Step-by-step explanation:
There’s 12 months in a year so
60 x 12 = 720
Tom has 750 so take away 720 that bill makes a year = 30
When ringing up a customer, a cashier needs 18 seconds to process payment as well as 1 second to scan each item being purchased. If it takes 20 seconds to ring up a customer, how many items are being purchased?
HELP ASAP!! WILL GIVE BRAINLIEST!!!! FULL ANSWERS ONLY!!!!!!
Find the x and y intercepts of the equation. Express your answers as points
5x+7y=-140
X-Intercept =
Y-Intercept =
Step-by-step explanation:
the answer is in the image above
PLS HELP ASAP !!!!!!!!!!!!
Answer:
D-780 squared inches
Step-by-step explanation:
you multiply 2(l)(w)+2(l)(h)+2(w)(h)
Answer:
Last option 780.
Step-by-step explanation:
To get the surface area for this you will need to get the area of each square that you see is in the net version. Once you do that you add them all together. Here is the math. . .
(4*25)+(4*10)+(4*25)+(10*25)+(10*25)+(4*10) = 780 total surface area.
If this looks confusing just look at the net version of the rectangular prism and you can see there is a duplicate of the different dimension triangles. These areas would be (4*25), (4*10), (10*25). There are a total of 3 different size triangles and all of them have duplicates. So we just multiply everything by 2
(4*25)+ (4*10)+(10*25) = 390 now multiply that by 2 and you get 780 again.
Hope the explanation helps :)
2. Denise took out a $16 000.00 loan from the bank to help pay for university. The bank offered an
annual interest rate of 5.6% compounded quarterly over a 3-year term. The entire loan is repaid
at the end of the 3-year term. Determine the total amount that Denise had to pay back.
graph the number that represents the situation on a number line. please help with this question i will mark you brainliest!
Answer:
OMGGGG OMGGG I NEEDTHIS QUESTION TOOOOOO
Let A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose an element of A is randomly selected. What is the probability that it belongs to {1, 2}U{2, 6, 7, 9}U{5, 6, 7).
============================================================
Explanation:
The set {1, 2}U{2, 6, 7, 9}U{5, 6, 7} simplifies to {1,2,5,6,7,9} after we combine everything and sort the values. We toss any duplicates.
Let B = {1,2,5,6,7,9}
There are 6 items in set B out of 10 items in set A.
The probability of landing in set B, if you pick something randomly from A, is 6/10 = 3/5
Answer:
3/5
Step-by-step explanation:
3.61 in cubic centimeters?
Answer:
59.157 cubic centimeters
find the value of x (URGENT/GIVING BRAINLIEST)
Answer:
B)10
Step-by-step explanation:
Because this is a right angle(indicated by the red box) the total measure should be 90°.
And based on that we say 5X +40=90
Subtract 40 from both sides to get 5x=50
And then divide both sides by 5 to get x=10
Answer:
x = 10°
Step-by-step explanation:
5x° + 40° = 90°
5x° = 90°-40°
5x°=50°
x°= 50°/5
x = 10°
Karen and Dale and Tom sent a total of 84 messages during the weekend. Dale sent six fewer messages and Karen and Tom sent four times as many as Karen. How many did they send each.
Answer:
Karen: 15; Dale: 9; Tom: 60
Step-by-step explanation:
"Karen and Dale and Tom sent a total of 84 messages during the weekend."
k + d + t = 84
"Dale sent six fewer messages than Karen"
d = k - 6
"Tom sent four times as many as Karen."
t = 4k
Substitute k - 6 for d and 4k for t in the first equation.
k + d + t = 84
k + k - 6 + 4k = 84
6k - 6 = 84
6k = 90
k = 15
d = k - 6 = 16 - 6 = 9
t = 4k = 4(15) = 60
Answer: Karen: 15; Dale: 9; Tom: 60
A chessboard is a square that has 8 rows and 8 columns of square spaces. If the side of a square space is 3.25 inches long, what is the area in square inches of the chessboard?
Answer:
676 square inches
a = L²
It has been established in the question that the length and the width of the chessboard has 8 rows an 8 columns respectively
length = with
rows = columns
8 × 3.25 = 26inches
AREA = L²
A = 26²
A = 676 square inches
The area in square inches of the chessboard given the side length of a square space is 676 inches².
What is the area of the chessboard?
A square is a quadrilateral with four equal sides.
The first step is to determine the area of a square space.
Area = length²
3.25² = 10.56 in²
The second step is to multiply the area of the square space by the number of squares.
8x 8 x 10.56 = 676 inches².
To learn how to determine the area of a square, please check: https://brainly.com/question/9030544
CRACK the CODE
2
Complementary * Supplementary Angles
D
(5x+8)
A
Angles A and B are
supplementary. If
MzB=101) What is
the MZA?
(3x+8)
с
offi+x)
(8x+5)
f
Angles A and B are
complementary. If
MZA=120, what is
the M2B2
ID
{ 720
(3x+3)
An angle measures
760. What is the
measure of its
complement?
6
(x+20)
(Ex-IS)
An angle measures
76. What is the
measure of its
supplement?
(14x-33)
(6x +13)
| K
35P
149° (13x+5)
J
(6
ECOLEX
Se
2019
Answer:
yea i dont know this one bro
Step-by-step explanation:
calculate the volume of each cone. Use 3.14 for π. Round the answer to the nearest hundredth is necessary.
Answer:
V = 29.31 cm^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h
V = 1/3 (3.14) (2)^2 (7)
V =29.30666
Rounding to the nearest hundredth
V = 29.31 cm^3
____ Is the amount of money owed in addition to the original amount
APR
Interest
APY
Principal
Answer:
APR INTEREST
THANKS ME LATUR
The slope of the line graphed below is -3.
true or false?
Answer:
False, the slope is POSITIVE 3.
What is the net price if a purchase would have come to $1,500 at the regular price, but a 3% discount applies to this purchase.
Step-by-step explanation:
100%-3%=97%
$1500*97%=$1455
Identify the image of XYZ for a composition of a 150 rotation and a 30 rotation both about point y
Answer:
hlw its jess your ans is here ↑ ↓
:- 150 rotation and the other 30 rotation about the same point is equivalent to 150+30 = 180
rotation about that point
Given vector u = (3, 1) and v = (2,-4), determine the value of v – 4u in
component form.
Answer:
(-10, -8)
Step-by-step explanation:
4u
Each component of vector u is multiplied by 4. So
u = (3, 1)
4u = (4*3, 4*1) = (12,4).
v – 4u
Subtraction of the components of vector v by the components of the vector 4u. So
v - 4u = (2, -4) - (12, 4) = (2-12, -4 - 4) = (-10, -8)
The value is (-10, -8)
I don’t understand stand this can somebody please help me
Answer:
C
Step-by-step explanation:
The radius is 7, but in the standard form for a circle, the radius is squared which means that the answer is NOT A and B.
So now you have only two choices, C and D both of which have the radius shown as 49 which is 7 squared.
The center is at (5,-1)
that means that x will be written as (x - 5)
And y will be written as (y + 1)
Note: the signs of the center always change to the opposite of what they were.
The answer is (x - 5)^2 + (y + 1)^2 = 49