Answer:
Step-by-step explanation:
Given that:
p = 0.61
If X is the the number of students in a randomly selected group of a sample size n = 50
The expected value and the standard deviation can be computed as follows:
The expected value E(X) = np
The expected value E(X) = 50 × 0.61
The expected value E(X) = 30.5
The required standard deviation = [tex]\sqrt{np(1-p)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(1-0.61)}[/tex]
The required standard deviation = [tex]\sqrt{30.5(0.39)}[/tex]
The required standard deviation = [tex]\sqrt{11.895}[/tex]
The required standard deviation = 3.4489
The required standard deviation = 3.45
(b) Fill in the missing quantity. (Round your answer to the nearest whole number.)
There is an approximately 2.5% chance that _____ or more teenagers in the group will shop at the mall during the next week.
From the given information:
Now, we can deduce that:
the mean = 30.5
standard deviation = 3.45
Using the empirical rule:
At 95% confidence interval;
[μ - 2σ, μ + 2σ] = [ 30.5 - 2(3.45) , 30.5 + 2(3.45)]
[μ - 2σ, μ + 2σ] = [ 30.5 - 6.9 , 30.5 + 6.9]
[μ - 2σ, μ + 2σ] = [ 23.6, 37.4]
The 2.5% of the observations are less than 95% confidence interval and 2.5% observations are greater than 95% confidence interval.
The required number of teenagers is = the upper limit of the 95% confidence interval = 37
There is an approximately 2.5% chance that __37___ or more teenagers in the group will shop at the mall during the next week.
Four items are purchased at prices of $5.30, $1.29, $.53, and $.68. Sales tax applies at 5% of the total purchase price. What is the total charge?
Answer:
$8.19
Step-by-step explanation:
1. Add the cost of the items together
5.3 + 1.29 + 0.53 + 0.68 = 7.8
2. Solve for 5% of the cost of the items
5% = 0.05
7.8 · 0.05 = 0.39
3. Add the sales tax to the price of the items
7.8 + 0.39 = 8.19
Explanation:
Add up the prices
5.30 + 1.29 + 0.53 + 0.68 = 7.80
This is the total amount before tax is added. To find the amount after tax, we multiply by 1.05 to get
1.05*7.80 = 8.19
Or a longer way is to find 5% of 7.80 getting 0.05*7.80 = 0.39 in the amount of tax owed, which is added on top of the previous total we got earlier. So we have 7.80 + 0.39 = 8.19
The use of the multiplier 1.05 is handy when you need to apply multiple percentage increases (it also works if you have multiple discounts as well).
Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *
12/24
Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.
Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24
Step Three: Add our new fractions: 3/24+8/24= 12/24
Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten
I hope I've help!
It’s question 14 I need help with please it’s due soon
if you are trying to work out -3/4 - (-1/4 - 1/2) then the answer is 0
What is the value of 2 in 9,274
Answer:
200
Step-by-step explanation:
4 is in the ones place so 4 just 4
7 is in the tens place so it is 70
2 is the hundreds place so 200
9 is in the thousands place so 9.000
For a data set with Mean -20, SD-3 find the Z scores for each of the following raw scores: 23, 17, 15, 22, 30. 23: 17: 15: 22: 30:
A. 23
B. 17
C. 15
D. 22
E. 30
4. Look at your result from the previous question in regards to raw score of 15
Answer:
A. 1
B. -1
C. -1.67
D. 0.67
E. 3.33
Step-by-step explanation:
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 20 , SD = 3 while x represents the individual values
A. 23
Z = (23-20)/3 = 3/3 = 1
B. 17
z = (17-20)/3 = -3/3 = -1
C. 15
z = (15-20)/3 = -5/3 = -1.67
D. 22
z = (22-20)/3 = 2/3 = 0.67
E. 30
z = (30-20)/3 = 10/3 = 3.33
3/4=x/20,find the value of 'x'
Answer:
[tex]\boxed{x=15}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4} =\frac{x}{20}[/tex]
[tex]\sf Cross \ multiply.[/tex]
[tex]4 \cdot x = 20 \cdot 3[/tex]
[tex]4x=60[/tex]
[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]
[tex]\frac{4x}{4} =\frac{60}{4}[/tex]
[tex]x=15[/tex]
Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers
Answer:
i.)1,2,3,4,6,12
ii).the number itself
iii.)1
Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n 1 is odd, (iii) 3n 1 is odd, (iv) 3n is even.
Answer:
Step-by-step explanation:
Hello,
If n is even, it means that we can find k integer such that n = 2 * k.
Then n+1=2*k+1 is odd.
3n+1=6k+1=2*(3k)+1 where 3k is an integer so 3n+1 is odd.
3n = 2*(3k) is even.
Besides, if n+1 is odd we can find an integer p so that n+1=2p+1 so n = 2p is even.
3n+1 is odd means that we can find an integer q such that 3n+1=2q+1 so 3n=2q as 3 is not dividable by 2, it means that n is a multiple of 2, then n is even.
3n is even means that we can write 3n = 2z where z is an integer and again it means that n is a multiple of 2 and then n is even.
Thank you.
what is a prime number
A number that can be divided exactly only by itself and 1.
For Eg:- 7, 10, 13.
Answer:
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:
Solve 13x + 14 = 12x -5 (make sure to type the number only)
Answer:
x = -19
Step-by-step explanation:
13x + 14 = 12x - 5
subtract 12x from both sides
x + 14 = -5
subtract 14 from both sides
x = -19
Answer:
x= -19
Step-by-step explanation:
13x+14=12x−5
Subtract 12x from both sides.
13x+14−12x=−5
Combine 13x and −12x to get x.
x+14=−5
Subtract 14 from both sides.
x=−5−14
Subtract 14 from −5 to get −19
x=−19
I need help with this please
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.
Answer:
the probability the die chosen was green is 0.9
Step-by-step explanation:
Given that:
A bag contains two six-sided dice: one red, one green.
The red die has faces numbered 1, 2, 3, 4, 5, and 6.
The green die has faces numbered 1, 2, 3, 4, 4, and 4.
From above, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) = [tex]\dfrac{1}{6}[/tex]
P (4 | green dice) = [tex]\dfrac{3}{6}[/tex] =[tex]\dfrac{1}{2}[/tex]
A die is selected at random and rolled four times.
As the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in the first dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]
= [tex]\dfrac{4!}{2!(4-2)!} ( \dfrac{1}{6})^4[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^4[/tex]
= [tex]6 \times ( \dfrac{1}{6})^4[/tex]
= [tex](\dfrac{1}{6})^3[/tex]
= [tex]\dfrac{1}{216}[/tex]
The probability of two 1's and two 4's in the second dice can be calculated as:
= [tex]\begin {pmatrix} \left \begin{array}{c}4\\2\\ \end{array} \right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
= [tex]\dfrac{4!}{2!(2)!} \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]6 \times ( \dfrac{1}{6})^2 \times ( \dfrac{3}{6})^2[/tex]
= [tex]( \dfrac{1}{6}) \times ( \dfrac{3}{6})^2[/tex]
= [tex]\dfrac{9}{216}[/tex]
∴
The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{216} \times \dfrac{1}{2} + \dfrac{9}{216} \times \dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{1}{432} + \dfrac{1}{48}[/tex]
The probability of two 1's and two 4's in both die = [tex]\dfrac{5}{216}[/tex]
By applying Bayes Theorem; the probability that the die was green can be calculated as:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216}}{\dfrac{5}{216}}[/tex]
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{0.5 \times 0.04166666667}{0.02314814815}[/tex]
P(second die (green) | two 1's and two 4's ) = 0.9
Thus; the probability the die chosen was green is 0.9
which of the following greatest
6+(-2)
6-(-2)
6×(-2)
6+(-2)
I need help with this question
Answer:
a. 2
b. x^2 + 10x + 26
c. x^2 + 2x + 2
Step-by-step explanation:
For each part, replace x with the value you are given and simplify.
f(x) = x^2 - 2x + 2
a.
f(2) = 2^2 - 2(2) + 2 = 2
b.
f(x + 6) = (x + 6)^2 - 2(x + 6) + 2
= x^2 + 12x + 36 - 2x - 12 + 2
= x^2 + 10x + 26
c.
f(-x) = (-x)^2 - 2(-x) + 2
= x^2 + 2x + 2
joe went to to the store and spent a total of $37 .84. if paid with a $50 then how much change did he get back?
Answer:
$ 12.16
Step-by-step explanation:
Spent = $ 37.84
Paid = $ 50
Change = $50 - $37.84
Change = $ 12.16
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Answer:
$12.16
Step-by-step explanation:
You must subtract his total from his payment. $50-$37.84=$12.16
Write an expression to represent the given statement. Use n for the variable. Three times the absolute value of the sum of a number and 6
Answer:
3 · |x+6|
Step-by-step explanation:
Write out what you see. "Three times" is 3 · something; "the absolute value of the sum of a number and 6" is |number + 6|. We'll use x for our number. Put it all together and you get 3 · |x+6|
The expression of the statement, Three times the absolute value of the sum of a number and 6 is [tex]\[3\left| n+6 \right|\][/tex] .
Representation of statement:Let n be the number.The sum of the numbers n and 6 is n+6.The absolute value of the sum of the numbers n and 6 is [tex]\[\left| n+6 \right|\][/tex].Hence, three times the absolute value of the sum of a number and 6 is [tex]\[3\left| n+6 \right|\][/tex].
Learn more about the representation of an expression:
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#SPJ2
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
Answer:
1. elements it contains = (1,3)
2. elements it contains = 35
3. elements it contains = 8
4. elements it contains = 17
Step-by-step explanation:
A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?
NB. Attached is the solution to the problems stated above
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
∫∫D(x2 + y2 + 2020)dxdy D: x2 +y2 +2ax ≤ 0 (a > 0)
Answer:
good morning
Step-by-step explanation:
hope u have a nice day
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
find the surface area of the prism HURRY HURRY
Answer:
should be 192
Step-by-step explanation:
What is 17,210,000,000 written in scientific notation?
Answer and Step-by-step explanation:
The answer is 1722.1 x [tex]10^8[/tex]
#teamtrees #PAW (Plant And Water)
Answer:
1.72x10^10
Step-by-step explanation:
POSITIVE EXPONENT: means a number is huge
NEGATIVE EXPONENT: indicates a number is teeny-tiny
A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19
Answer:
C.
Step-by-step explanation:
16,299.99*0.065=1059.50
At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?
Answer:
£32 in total for the top and two trousers
Step-by-step explanation:
The price for a top In the "cloth for you" shop= £10
The price for a bermuda trouser In the "cloth for you" shop= £12
There is a 20% discount on tops
The price If I bought one top and would trouser will be
(10-(0.2*10)) for the top
2(12) for the trouser
Total= (10-(0.2*10))+ 2(12)
Total = 10-2+24
Total = £32
So I spent £32 in total for the top and two trousers
The double number line shows that Toni can type 180 words in
2 minutes.
Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?
Answer:
120 words
Step-by-step explanation:
as a ratio it's
2:180
In real life the longer you do something the more words you type
so since you can't get to 3 from 2 easily you go to 1 instead.
2:180
1:360
3:120
Use spherical coordinates. Evaluate e x2 + y2 + z2 dV, E where E is enclosed by the sphere x2 + y2 + z2 = 25 in the first octant.
Answer:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \frac{\pi (17e^5 - 2)}{2}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Method [Integration by Parts]:
[tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
Multivariable Calculus
Triple Integrals
Cylindrical Coordinate Conversions:
[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]Spherical Coordinate Conversions:
[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]
Step-by-step explanation:
*Note:
Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.
I will not show/explain any intermediate calculus steps as there isn't enough space.
Step 1: Define
Identify given.
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV[/tex]
[tex]\displaystyle \text{Region E:} \ x^2 + y^2 + z^2 = 25 \ \text{bounded by first octant}[/tex]
Step 2: Integrate Pt. 1
Find ρ bounds.
[Sphere] Substitute in Spherical Coordinate Conversions:Find θ bounds.
[Sphere] Substitute in z = 0:Find φ bounds.
[Circle] Substitute in Cylindrical Coordinate Conversions:Step 3: Integrate Pt. 2
[Integrals] Convert [Integral Conversion - Spherical Coordinates]:We evaluate this spherical integral by using the integration rules, properties, and methods listed above:
[tex]\displaystyle \begin{aligned} \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta \\ & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {\bigg[ (\rho^2 - 2 \rho + 2) e^{\rho} \sin \phi \bigg] \bigg| \limits^{\rho = 5}_{\rho = 0}} \, d\phi \, d\theta\end{aligned}[/tex]
[tex]\displaystyle \begin{aligned}\iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {(17e^5 - 2) \sin \phi} \, d\phi \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {\bigg[ -(17e^5 - 2) \cos \phi \bigg] \bigg| \limits^{\phi = \frac{\pi}{2}}_{\phi = 0}} \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {17e^5 - 2} \, d\theta \\& = (17e^5 - 2) \theta \bigg| \limits^{\theta = \frac{\pi}{2}}_{\theta = 0} \\& = \frac{\pi (17e^5 - 2)}{2}\end{aligned}[/tex]
∴ the given integral equals [tex]\displaystyle \bold{\frac{\pi (17e^5 - 2)}{2}}[/tex].
---
Learn more about spherical coordinates: https://brainly.com/question/16415822
Learn more about multivariable calculus: https://brainly.com/question/4746216
---
Topic: Multivariable Calculus
Unit: Triple Integrals Applications
Can someone help me?
Answer:
7w
Step-by-step explanation:
According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 341 community college students at random and finds that 147 of them have a smart phone. Then in testing the hypotheses:
H0: p = 0.4 versus
Ha: p > 0.4,
what is the test statistic?
z =________________. (Please round your answer to two decimal places.)
B.)
According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 349 community college students at random and finds that 138 of them have a smart phone. In testing the hypotheses:
H0: p = 0.33 versus
Ha: p > 0.33,
she calculates the test statistic as z = 2.5990.
Then the p‑value =________________ .
(Please round your answer to four decimal places.)
Answer:
z = 1.17
P - value = 0.0047
Step-by-step explanation:
A.
From the given information;
H0: p = 0.4 versus
Ha: p > 0.4,
Let's calculate the population proportion for the point estimate;
the population proportion [tex]\hat p[/tex] = 147/341
the population proportion [tex]\hat p[/tex] = 0.431085
However; the test statistics can therefore be determined by using the formula:
[tex]z = \dfrac{\hat p - p_o}{\sqrt{\dfrac{p_o(1-p_o)}{n}}}[/tex]
[tex]z = \dfrac{0.431085 - 0.40}{\sqrt{\dfrac{0.40(1-0.40)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.40(0.60)}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.24}{341}}}[/tex]
[tex]z = \dfrac{0.031085}{\sqrt{7.03812317 \times 10^{-4}}}[/tex]
[tex]z = \dfrac{0.031085}{0.0265294613}[/tex]
z = 1.1717
z = 1.17 to two decimal places
B.)
The null and the alternative hypothesis is given as:
H0: p = 0.33 versus
Ha: p > 0.33,
The z = 2.5990.
The objective here is to determine the p-value from the z test statistics.
P - value = P(Z > 2.5990)
P- value = 1 - P(Z < 2.5990)
P - value = 1 - 0.9953
P - value = 0.0047
What is the rise over run for the slope -11/9
Answer: 11 down and 9 right
Step-by-step explanation:
Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down
and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.
Given slope = -11/9
the numerator is -11 so the "rise" is DOWN 11 units
the denominator is 9 so the "run" is RIGHT 9 units
15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! 15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? Equation 1: 2x - 3y = 12 Equation 2: -2x + y = 8 A. Add the left side of equation 2 to the left side of equation 1. B. Multiply equation 2 by 3. Then substract the result from equation 1. C. Add equation 2 to equation 1.
Answer:
(A)
Step-by-step explanation:
That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.
Please tell me if I got it wrong. I really hope it is correct.
A. Add the left side of equation 2 to the left side of equation 1.
B. Multiply equation 2 by 3. Then subtract the result from equation 1.
C. Add equation 2 to equation 1.