Using the normal distribution and the central limit theorem, it is found that there is a 0.24 = 24% probability of observing a difference this large or larger.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].When two variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.In this problem, for each sample, the mean and standard error are given by:
[tex]\mu_I = 0.4, s_I = \sqrt{\frac{0.4(0.6)}{75}} = 0.0566[/tex]
[tex]\mu_{II} = 0.4, s_{II} = \sqrt{\frac{0.4(0.6)}{90}} = 0.0516[/tex]
Hence, for the distribution of differences, the mean and the standard error are given by:
[tex]\mu = \mu_I - \mu_{II} = 0.4 - 0.4 = 0[/tex]
[tex]s = \sqrt{s_I^2 + s_{II}^2} = \sqrt{0.0566^2 + 0.0516^2} = 0.0766[/tex]
The probability of observing a difference this large or larger is given by P(|Z| > Zx), in which Zx is the z-score when X = 0.0766. Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.09 - 0}{0.0766}[/tex]
Z = 1.175.
Hence the probability is P(|Z| > 1.175), which is 2 multiplied by the p-value of Z = -1.175. Then:
2 x 0.12 = 0.24.
0.24 = 24% probability of observing a difference this large or larger.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
parts of an algebraic expression separated by plus or minus signs are
Answer: called tthe term of an algebraic expression.
Step-by-step explanation: We know an algebraic expression is a collection or combination of constant and variables of one or more terms, which are separated by the fundamental operations (+, –, × and ÷).Some of the examples of algebraic expression are 7b + 5m, 5x + 3y + 10, 5x/y + 3, x + y + z, etc.Terms of an algebraic expression:Each part of an algebraic expression which are separated by plus sign (+) or minus sign (-) is called the term of an algebraic expression. It’s important to remember that the division sign (÷) or multiplication sign (×) does not separate the terms of an algebraic expression.Examples of algebraic expressions and their terms:
(i) x + 10
We observe that the number of terms used in the expression x + 10 is 2. The terms are x and 10.
(ii) 5m + 2n - 7
We observe that the number of terms used in the expression 5m + 2n – 7 is 3. The terms are 5m, 2n and 7.
(iii) 3a/b
We observe that the number of term used in the expression 3a/b is 1. The term is 3a/b.
(iv) 3xy + 7xz + 2yz - 6
We observe that the number of terms used in the expression 3xy + 7xz + 2yz - 6 is 4. The terms are 3xy, 7xz, 2yz and 6.
) 2abc + 1
We observe that the number of terms used in the expression 2abc + 1 is 2. The terms are 2abc and 1.
Therefore, the algebraic expressions are either simple or compound.
(i) Simple algebraic expressions consist of one term.
(ii) Compound algebraic expressions consist of two or more terms.
How many feet are in 1 yard?
Answer:
Step-by-step explanation:
there are 3 feet in a yard
1 foot = 12 inches
3 feet = 36 inches
36/12 = 3 feet
A college student takes out a $ 7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet): a. if the bank charges 3.8% interest each year? b. if the bank charges 5.3% interest each year?
Answer:
Substitute P=7500, r=0.053 and t=1 in equation (1). Therefore, the balance of the loan be after one year is $7897.5
Select the expression that represents the following problem: A glass hols 1/4 liter of liquid. How many glasses of liquid are in 5 liters
1 glass..........1/4 liter
n glass.......... 5 liters
n = 1 x 5 : 1/4
n = 5 x 4
so there are 20 glasses
wich one' is the right answer need help
Answer:
C
Step-by-step explanation:
because density equal all the rest
Can anyone help?! Its for geometry. Please show your work and the answer for x
I need help please….
Answer:
C. 7/20
Step-by-step explanation:
There are 20 arrival times on the table.
7 of those twenty are before 8:20.
p(before 8:20) = 7/20
Answer: C. 7/20
NEED ANSWERS QUICKLY! CORRECT ONE GETS BRAINLIEST
Write a mixed number between 5 and 6, and then write its reciprocal.
Answer: 11/2
Reciprocal: 2/11
Step-by-step explanation: 11/2 is 5.5 (between 5 and 6) the reciprocal or 11/2 is 2/11
What is the area Of the desk
Answer:
28 ft²
Step-by-step explanation:
area of the desk = (5×4) + (4×2) = 20 + 8 = 28 ft²
Answer:
28
Step-by-step explanation:
5 times 4 = 20
4 times 2= 8
20 plus 8=28
(2)•(4.5)=? Fill in the missing number in the equation
Answer:
9
Step-by-step explanation:
twice the value of 4.5 equals 9
If 12 workers can dig a tunnel in 100 days, how long will it take 20 workers to dig the tunnel
Answer:
60 days.
Step-by-step explanation:
This is a proportion question. You compare two ratios. Unfortunately it is an inverse ratio.
12 = k/100 Multiply both sides by 100
1200 = k
20 = k/x Multiply both sides by x
20x = k
20x = 1200 Divide by 20
20x/20 = 1200/20
x = 60 days.
An inverse proportion works by making a constant k. The constant k makes the days shorter when the number of people increases. You should expect that. More people , less time.
A kite is inscribed in a square with a side length of 9 units. What is the area of the kite? 27. 5 square units 36. 0 square units 40. 5 square units 45. 0 square units.
45. 0 square units.
The area of the kite is 40.5 unit square.
The side of the kite inscribed in square is 9
We have to find the area of the kite
What is the formula for the area of the kite?The area of a kite is,
[tex]A = (d_1d_2) / 2[/tex]
Where [tex]d_1[/tex] and [tex]d_2[/tex] are the diagonals of the kite.
The kite is inscribed in the square, and the sides of the square are 9 units, the diagonals of the kite are both 9 units.
Therefore we get,
[tex]d_1 = 9 units[/tex]
[tex]d_2 = 9 units[/tex]
[tex]A = (9units \times 9units) / 2[/tex]
[tex]A = 81units^2 / 2[/tex]
[tex]A = 40.5 units^2[/tex]
So the third option is correct .
Therefore ,The area of the kite is 40.5 unit square.
To learn more about the area of the kite visit:
https://brainly.com/question/16424656
Find the 10th term of the following geometric sequence 6,24,96,384,…
Answer:
1572864
Step-by-step explanation:
the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]
where an = nth term, a1 = first term , r = common ratio and n = term position.
here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )
so a1 = 6 , r = 4 and n = 10
using these values we plug them into the rule
recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]
==> plug in a1 = 6 , r = 4 and n - 10
[tex]a_1_0=6(4)^1^0^-^1[/tex]
==> subtract 10 and 1
[tex]a_1_0=6(4)^9[/tex]
==> simplify exponent
[tex]a_1_0=6(262144)[/tex]
==> simplify multiplication
[tex]a_1_0=1572864[/tex]
and we are done!
Note:
the common ration was found by dividing the first term by the next term
Given the polar coordinates (4,-pi/3) which of the following rectangular coordinate pairs represents the same point?
a) (-2,2sqrt3)
b) (2,-2sqrt3)
c) (2sqrt3,-2)
d) (2sqrt3, 2)
The rectangular point that represents (4, - pi/3) is the one in option b: (2, -2√3).
How to change the coordinates?
For a point (x, y), the polar coordinates are:
R = √(x^2 + y^2)θ = atan(y/x).Then we must have:
R = 4 = √(x^2 + y^2)
Notice that for all the given points we have the radius equal to 4, so the only part that we care is the angle one:
-pi/3 = Atan(y/x)
tan(-pi/3) = y/x = -1.73
So, y and x must have different signs, and because the angle is negative, we will say that the y-component must be negative.
So the correct option will be b: (2, -2√3)
y/x = -2*√3/2 = √3 = -1.73
If you want to learn more about polar coordinates, you can read:
https://brainly.com/question/14965899
Answer: Quiz answer Unit 4 lesson 6
all answers are right
Step-by-step explanation:
1.) Given the polar coordinates (4,-pi3)which of the following rectangular coordinate pairs represents the same point?
Answer is B: (2,-2sqrt3)
2.) Given the rectangular coordinates (-5 5) which of the following polar coordinate pairs in, radians, represent the same points?
the correct option is D. (5√2,3π4)
3.)Rewrite in rectangular form: r=8 sin theta -2 cos theta.
Answer:
The equation in rectangular form is:
4.)Rewrite in polar form: x^2+y^2-6y-8=0
the Answer is B. r^2=6r sin 0+8
5.)The graph of r=-9 cos theta has which of the following characteristics?
Answer:
"circle; diameter of 9; center at (-4.5,0)"
6.)Which conic section is represented by the polar equation r=1/4-6 cos theta?
Answer:
Option 2 - Hyperbola
7.)Identify the horizontal and vertical intercepts of the limaçon represented by the equation r=7+3 cos theta ?
Answer:
vertical intercepts: (7, pi/2) and (-7, pi/2)
horizontal intercepts: (10,0) and (-4,0)
8.) Classify the limaçon represented by the equation r=1/2-1/2 sin theta.
A. Cardioid
9.)Write the equation for the graph of the rose curve.
answer C: r=9 sin 4 theta
10.) Write the equation for the graph of the lemniscate.
answer D: r^2=-49 sin 2theta
(pls don't report for me not explain it took a lot of time typing this and im just trying to help people have less stress on their shoulders :p )
What is 2+2 I think it’s still 2 but I am not sure yet
Answer:
it actually equals 5
Step-by-step explanation:
the reason it equals 5, is because there are 5 variables in there, so because of the addition sign, it becomes 1+1+1+1+1=5. you cannot prove me wrong.
Answer:
the correct answer is 4
Step-by-step explanation:
2 + 2 = 4
hope this helps
have an awesome day -TJ :)
The function P(x) is mapped to I(x) by a dilation in the following graph.
Which answer gives the correct transformation of P(x) to get to I(x)?
The correct transformation of P(x) to get I(x) is I(x) = 2P(x)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
From the graph of I(x) and P(x), we can see that:
I(x) = 2P(x)
The correct transformation of P(x) to get I(x) is I(x) = 2P(x)
Find out more on transformation at: https://brainly.com/question/1548871
An office decreases paper waste by
35%. Originally the office produces
w pounds of waste.
Part A
reads forx nights? Which expression represents the
waste reduction?
A. w - 35
B. 1.35w
C. 0.35w
D. w-0.35w
Part B
How much paper waste do they
produce now, if they originally
produced 8 pounds per month?
The expression that represents waste reduction is w - 0.35x.
The paper waste produced now is 5.2 pounds per month.
What is the expression that represents waste production?The exression that represents waste production is the total amount of waste generated less athe reduction in waste.
w - 0.35x
Waste now produced = 8 - 0.35 x 8 = 5.2 pounds
To learn more about mathematical expressions, please check: https://brainly.com/question/11980704
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,8) and perpendicular to 3x + 5y = 1
Step-by-step explanation:
a) 2y = 3x + 4
b) given the perpendicular
3x + 5y = 1
5y = 1 - 3x
y = 1/5 - 3x/5
m¹ = -3/5
perpendicular
m¹m² = -1
-3m²/5 = -1
m² = 5/3
so (1,8)
x¹ = 1 y¹ = 8
m² = (y - y¹)/(x - x¹)
5/3 = (y - 8)/(x - 1)
5x - 5 = 3y - 24
3y - 5x + 5 - 24 = 0
3y = 19 + 5x
What is the area of rectangle PQRS?
The area of a rectangle is l*w. We have the length as 4.5 in and we can find the width by doing 3+2+4.5 = 9.5 in.
Then, we multiply them. 4.5*9.5 = 42.75 inches²
Determine the intercepts of the line.
Do not round your answers.
Y=5x-13
Answer:
y intercept:(0,-13)
x intercept: (13/5,0)
Step-by-step explanation:
The way we find intercepts (both x and y) is to plug in zero.
x int:
We set y to 0:
0=5x-13
add thirteen to both sides
13=5x
x=13/5
y int:
set x to zero
y=5(0)-13
y= - 13
please help if you are good at maths
on the image.
Answer:
x=74
Step-by-step explanation:
if angle ABE = 148. then, angle EBC = 32
and for angle ECB an BEC,
180-32 = 148
148/2 = 74
so, angle ECB and angle BEC = 74
we know, angle BCE and angle CEF are equal because they are alternate angles
so, x = 74
=
O FRACTIONS
Fraction multiplication
Multiply. Write your answer as a fraction in simplest form.
3 6
Х
4 5
OL
Х
?
Answer:
Perhaps 2/5, if I understand your question.
Step-by-step explanation:
i don't understand the format of your question:
"3 6
Х
4 5
OL
Х
?"
Is this meant to be (3/6)*(4/5) ??
If so:
(3/6)*(4/5) = (12/30)
(12/30) = 6/15
6/1`5 = 2/5
please me please pls
the line passes through the point ( - 8 ; - 2)
so f(-8) = - 2
what is the area of this triangle?
A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150. 00 with a standard deviation of $30. 20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2. 5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test? The customers spend more than the national average in his store. The manager should decrease prices in his store. The customers do not spend more than the national average in his store. The customers in his store just come from a rich neighborhood.
The valid conclusions for the manager based on the considered test is given by: Option
When do we perform one sample z-test?One sample z-test is performed if the sample size is large enough (n > 30) and we want to know if the sample comes from the specific population.
For this case, we're specified that:
Population mean = [tex]\mu[/tex] = $150Population standard deviation = [tex]\sigma[/tex] = $30.20Sample mean = [tex]\overline{x}[/tex] = $160Sample size = n = 40 > 30Level of significance = [tex]\alpha[/tex] = 2.5% = 0.025We want to determine if the average customer spends more in his store than the national average.Forming hypotheses:
Null Hypothesis: Nullifies what we're trying to determine. Assumes that the average customer doesn't spend more in the store than the national average. Symbolically, we get: [tex]H_0: \mu_0 \leq \mu = 150[/tex]Alternate hypothesis: Assumes that customer spends more in his store than the national average. Symbolically [tex]H_1: \mu_0 > \mu = 150[/tex]where [tex]\mu_0[/tex] is the hypothesized population mean of the money his customer spends in his store.
The z-test statistic we get is:
[tex]z = \dfrac{\overline{x} - \mu_0}{\sigma/\sqrt{n}} = \dfrac{160 - 150}{30.20/\sqrt{40}} \approx 2.094[/tex]
The test is single tailed, (right tailed).
The critical value of z at level of significance 0.025 is 1.96
Since we've got 2.904 > 1.96, so we reject the null hypothesis.
(as for right tailed test, we reject null hypothesis if the test statistic is > critical value).
Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.
Learn more about one-sample z-test here:
https://brainly.com/question/21477856
Answer:
A
Step-by-step explanation:
The scores at a golf course recorded last year followed a normal distribution with mean 78 and
standard deviation 11. you choose an srs of 15 scores and calculate xbar = mean score. which of
the following are the mean and standard deviation of the sampling distribution of x bar?
Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.
What does the Central Limit Theorem state?It states 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].
In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].
Then, considering samples of n = 15, we have that the standard deviation is given by:
[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
531x22 long mutipulcation
Answer:
11,682 the answer is that hope you get a A!
531
×22
+1062
+1062
=11682
Therefore:
531 × 22 = 11,682
A flat-bottomed ice cream waffle cup is shaped like a 72 mm tall cone with a 42 mm diameter opening at the top, but with the bottom 24 mm of the cone replaced by a flat waffle bottom with a 14 mm diameter. to the nearest square millimeter, what area of waffle does the cone have?
a.) 4002
b.)4398
c.)4552
d.)4157
The area of waffle in the cone is the amount of space covered by the waffle
The cone has 5630 square millimeter of waffle
How to determine the surface area?
The surface area of a cone is calculated using:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
For the complete 72 mm tall cone, we have:
Height (h) = 72 mm
Radius (r) = 42 mm/2 = 21 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 21 * (21+[tex]\sqrt{[/tex](72^2 + 21^2))
Evaluate
A = 3.142 * 21 * (21+75)
A = 6334.272
When the cone is cut at the top, we have:
Height (h) = 24 mm
Radius (r) = 14 mm/2 = 7 mm
So, the surface area is:
A = πr * (r+[tex]\sqrt{[/tex](h^2 + r^2))
A = 3.142 * 7 * (7+[tex]\sqrt{[/tex](24^2 + 7^2))
Evaluate
A = 3.142 * 7 * (7 + 25)
A = 703.808
Calculate the difference (d) between the areas
d = 6334.272 - 2.5*703.808
Evaluate
d = 5630.464
Approximate
d = 5630
Hence, the cone has 5630 square millimeter of waffle
Read more about surface area at:
https://brainly.com/question/6613758
What is m ZLMN?
OA) 40°
OB)
B) 60°
OC) 75°
OD) 80°
Answer:
A
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
100° is an exterior angle of Δ MLN , then
∠ LMN + 60° = 100° ( subtract 60° from both sides )
∠ LMN = 40°
HAPPY BIRTHDAY!
You have decided to give your best friend a bag of red
and green marbles for his birthday. Your friend likes
green marbles better than red ones, so the bag has
twice as many green marbles as red. The label on the
bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write a
system of equations for this problem. Then solve the
problem using any method you like. Be sure to check
your solution
Answer:
56
Step-by-step explanation:
(84÷3) · 2 = x
28 · 2 = 56
Hope that helps!