Final answer:
The correct statement about the conditions for performing a one-sample z test for the population is that we can't determine if the conditions have been met until we have the sample proportion, p hat.
Explanation:
The correct statement about the conditions for performing a one-sample z test for the population is:
a. We can’t determine if the conditions have been met until we have the sample proportion, p hat.
When performing a hypothesis test of a single population proportion, the conditions for a binomial distribution need to be met. These conditions include a certain number of independent trials, success or failure outcomes, and each trial having the same probability of success. In addition, the shape of the binomial distribution should be similar to the shape of a normal distribution, which is ensured when np and nq are both greater than five. Therefore, the conditions cannot be definitively determined until the sample proportion, p hat, is known.
The Large Counts condition is met (np >= 10, n(1-p) >= 10), allowing the z-test. Other conditions are satisfied, validating the test.
Therefore, the correct answer is: **d. The test cannot be performed because the Large Counts condition has not been met.**
To perform a one-sample z-test for the population proportion, we need to check certain conditions:
1. **Random Sample**: The sample should be chosen randomly from the population to ensure that it is representative.
2. **Normality of Population**: There are two criteria for this condition:
- If the population distribution is approximately normal, we can proceed.
- If the population distribution is not normal, the sample size should be large enough (n x p >= 10 and n x (1-p) >= 10) to ensure that the sampling distribution of the sample proportion is approximately normal by the Central Limit Theorem.
3. **Independence**: Each observation in the sample should be independent of the others.
Given:
- Sample size (n) = 30
- Population proportion (p) = 0.04
We need to check if these conditions are met.
a. **We can’t determine if the conditions have been met until we have the sample proportion, p hat.**
- This statement is incorrect because we can still check the conditions without knowing the sample proportion.
b. **The test cannot be performed because the Random condition has not been met.**
- This statement is incorrect because the problem states that the buyer took a random sample of 30 apples, so the Random condition has been met.
c. **All conditions for performing the test have been met.**
- This statement is incorrect because we haven't checked the Large Counts condition yet.
d. **The test cannot be performed because the Large Counts condition has not been met.**
- To check the Large Counts condition, we need to verify whether the sample size is large enough to ensure that the sampling distribution of the sample proportion is approximately normal.
- The Large Counts condition is met if both np >= 10 and n(1-p) >= 10.
- Here, n = 30 and p = 0.04
- np = 30 x 0.04 = 1.2
- n(1-p) = 30 x (1 - 0.04) = 28.8
- Both np and n(1-p) are greater than or equal to 10.
- So, the Large Counts condition is met.
Therefore, the correct answer is: **d. The test cannot be performed because the Large Counts condition has not been met.**
geckos and iguanas are both lizards. The length of the average gecko is about two fifths of the length of average iguana. Geckos are about 10 in. long. What is the lenth of an average iguana.
Answer:
25 in.
Step-by-step explanation:
Since we know geckos are 2/5 of an Iguana's length, we need to find the length of 1/5.
So if 10 in. is 2/5, 5 in, is 1/5.
Now, since the denominator is 5, we multiply 5 in. by 5.
5x5=25 in.
25 in. is the length of an average Iguana.
What is 15990000 written as scientific notation
Answer:= 1.599 × 107
Step-by-step explanation:
here you go
find the additive inverse of -7+5i.
Answer:
Required additive inverse is [tex]-7-5i[/tex].
Step-by-step explanation:
Given number is [tex]-7+5i[/tex].
Now we need to find about what is that additive inverse of the given number [tex]-7+5i[/tex].
We know that if complex number is [tex]a+bi[/tex] then it's additive inverse is given by [tex]a-bi[/tex].
Basically we need to change the sign of imaginary term.
imaginary term in given number [tex]-7+5i[/tex] is +5i.
Changing sign of +5i gives -5i.
Hence required additive inverse is [tex]-7-5i[/tex].
Plsssss helppppppppppp
Answer:
B
Step-by-step explanation:
A parabola is symmetric about the vertex point. The x-coordinate of the vertex is 4.6.
So the parabola has 1 intersection point at x = 0 (origin as shown) and the line of symmetry is at x = 4.6. That is, from 0 to 4.6, it is 4.6 units. Hence, the other intersection point at the x-axis should be from 4.6 to 4.6 units to the right.
Hence, 4.6 + 4.6 = 9.2
The x-intercept would be (9.2, 0)
Correct answer is B
Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 2.25 minutes?
Answer:
Step-by-step explanation:
x / 2.25 seconds = 28 times / 12 seconds
multiply by sides by 2.25 seconds
x / 2.25 seconds * 2.25 seconds = 28 times / 12 seconds * 2.25 second
x = 2.3333333 times/ second * 2.25 seconds
x = 5.8333
Answer:
315 times
Step-by-step explanation:
We know that the friend can clap his hands 28 times in 12 seconds. First, we need to know how many times can he clap his hands in 1 second:
To do it we have to divide the times he can clap his hands by the time in seconds:
28/12 = 2.333333
He can clap his hands 2.333333 times in 1 second:
Now we want to know how many times will he clap his hands in 2.25 minutes
We have to change 2.25 minutes into seconds:
1 (minute) = 60 (seconds in 1 minute)
2.25 (minutes) * 60 (seconds in 1 minute) = 135 seconds
After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:
2.3333333 times * 135 seconds = 315
315 times in 2.25 minutes
Can someone check over this? And explain if it's wrong?
Answer:
You are correct!
:D
Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle? Explain why or why not.
Answer:
24, 32, 40 can be the lengths of the three sides of a right triangle
Step-by-step explanation:
Pythagoras theorem:
c^2 = a^2 + b^2
40^2 = 1,600
32^2 + 24^2 = 1024 + 576 = 1,600
If the square of the length of the hypotenuse (longest side length) is equal to the sum of the squares of the lengths of the other two sides then it's a right triangle
So
40^2 = 32^2 + 24^2
1,600 = 1,600
24, 32, 40 can be the lengths of the three sides of a right triangle
WHAT IS 6 x 6 x 6 x 6 x 6 is exponet form
Answer:
Exponent of 5
Step-by-step explanation:
Because there are 5 6s it would be 6 to the exponent of 5.
Given, 6×6×6×6×6
Have to write in Exponent form
So....Its given that there are 5 six so..we can write is as
[tex] = {6}^{5} [/tex]
Hope itz help!!✌☑️If the bases of an isosceles trapezoid have lengths of 11 and 24, what is the length of the median? A. 17.5 units B. 35 units C. 13 units D. 6.5 units
Answer:
Option A. [tex]17.5\ units[/tex]
Step-by-step explanation:
we know that
The measure of the median is the semi-sum of the bases
so
[tex]\frac{1}{2}(11+24)=17.5\ units[/tex]
Answer:
17.5
Step-by-step explanation:
1/2(11+24)=17.5
The number of DVDs in a random person’s home collection is counted for a sample population of 80 people. The mean of the sample is 52 movies; the entire population is known to have a standard deviation of 12 movies. Assuming a 99% confidence level, find the margin of error.
Answer:
[tex]E = 3.46\ movies[/tex]
Step-by-step explanation:
The formula to find the error is:
[tex]E = z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}[/tex]
Where:
[tex]\sigma[/tex] is the standard deviation
n is the sample size
So
n = 80 people
[tex]\sigma[/tex] = 12 movies
Then
[tex]1- \alpha[/tex] = confidence level = 0.99
[tex]\alpha= 1-0.99[/tex]
[tex]\alpha = 0.01\\\\\frac{\alpha}{2} = 0.005[/tex]
We look for the Z value: [tex]Z_{0.005}[/tex]
[tex]Z_{0.005}=2.58[/tex] Looking in the normal standard tables
Therefore:
[tex]E =2.58*\frac{12}{\sqrt{80}}\\\\E = 3.46\ movies[/tex]
A 4-digit number ends in 3. If you put the number 3 in the first position, the number will decrease by 738. Find the original 4-digit number?
Answer:
4153
Step-by-step explanation:
(x-3)/10 + 3000 = x-73
(x-3)/10 = x - 3738
x-3 = 10x - 37380
x = 10x - 37377
-9x = -37377
x = 4153
: P
Answer:
4153
Step-by-step explanation:
Let the original number be x
First, you subtract 3 from the original number. This removes 3 from the last digit, but leaves a zero there.
Now to remove the zero, you divide by 10.
Finally, to put the 3 at the first position, you add 3000.
Now Moving the last digit, 3, to the first position the number becomes :[tex]\frac{x-3}{10}+3000[/tex]
We are given that the number will decrease by 738.
A.T.Q
[tex]\frac{x-3}{10} + 3000 = x-738[/tex]
[tex]\frac{x-3}{10}= x - 3738[/tex]
[tex]x-3 = 10x - 37380[/tex]
[tex]x = 10x - 37377[/tex]
[tex]-9x = -37377[/tex]
[tex]x = 4153[/tex]
Hence the original 4-digit number is 4153.
please help i really need help
Answer:
142 degrees
Step-by-step explanation:
Since LON is 180 degrees...
9x - 91 + 6x + 76 = 180
15x - 15 = 180
15x = 165
x = 11
MON = 6(11) + 76
MON = 66 + 76
MON = 142
Find the product. Write your answer in exponential form. 2^-8*2
Answer:18446744073709600000
Step-by-step explanation:
2^-8*2=2^64=
what is 25 1/2 × 5 –3 = 5 x
Answer:
25 1/2 × 5 - 3 = 5x
51/2 × 5 - 3 = 5x
255/2 - 3 = 5x
255/2 - 6/2 = 10x/2
255 - 6 = 10x
249 = 10x
x = 249/10 = 24.9
The value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex] is x=24.9
What is the value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex]?Given:
An equation is given as [tex]25\frac{1}{2} * 5 -3 = 5x[/tex].Find:
The value of x.Solution:
The given equation is [tex]25\frac{1}{2} * 5 -3 = 5x[/tex]
Now, solving the equation, we get;
[tex]25\frac{1}{2} * 5 -3 = 5x[/tex]
[tex]\frac{51}{2} *5 - 3 =5x[/tex]
Now, multiplying the 51/2 with 5, we get;
[tex]\frac{255}{2} - 3 = 5x[/tex]
Now, we will take lcm and we get;
[tex]\frac{255-6}{2} = 5x[/tex]
[tex]\frac{249}{2} = 5x[/tex]
Now, multiplying with 2 on both sides of the equation, we get;
249 = 10x
Now, dividing by 10 into both sides of the equation, we get;
x = 24.9
Hence, the value of x in the equation [tex]25\frac{1}{2} * 5 -3 = 5x[/tex] is x=24.9
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Find the area and perimeter of the triangle below if a = 164 feet, b=221 feet, c=352 feet, and h=76 feet
Answer:
Perimeter=737 feets
Area=13542.6 ft²
Step-by-step explanation:
Well assuming that a,b,c are the three sides of the triangle and h is the height then;
Perimeter=distance around the figure
P=164+221+352= 737 feet
Area of a triangle given three sides is calculated using the formulae;
Area=√s (s-a) (s-b) (s-c) where s=(a+b+c)/2
Finding s;
s=(164+221+352)/2 =368.5 feet
Finding the area
A= √ 368.5 (368.5-164) (368.5-221) (368.5-352)
A=√368.5 (204.5) (147.5) (16.5)
A= 13542.6 ft²
If mike only has 100 dollars to spend on games, how many $20 games can he afford to buy?
Answer: 5
Step-by-step explanation: If Mike Only has $100 To Spend On Games, He Can Buy 5 Games Because We Multiply 20 By 5 To Get A Product Of 100.
Therefore, Mike Can Afford 5 Games With No Money Left.
Have A Fantastic Day!
Be Safe,
Eric
Mike can afford to buy 5 $20 games.
To determine how many $20 games Mike can afford to buy with $100, we divide the total amount of money he has by the cost of one game.
Total money Mike has = $100
Cost of one game = $20
Number of games Mike can afford = Total money / Cost of one game
Number of games Mike can afford = $100 / $20
Number of games Mike can afford = 5
Therefore, Mike can buy 5 games with $100.
Please help me with this and thank you
Answer:
The answer is D
Step-by-step explanation:
(12 + 6) x (11 - 7) = 72
18 x 4 = 72
72 = 72
The answer is D
Kim is making a bouquet for her friend. She used x tulips and some daffodils in the bouquet. The number of daffodils is equal to the square root of the number of tulips. If the total number of flowers in the bouquet is 20, find the number of tulips.
5
16
20
4
Answer:
16
Step-by-step explanation:
So the number of tulips (t) plus the number of daffodils (d) should equal up to 20. So if we write that as an equation, it would t + d = 20. So now we have to find what two numbers could add up to 20, but let's not forget that the number of daffodils is equal to the square root of the number of tulips.
So now we have to find a number when added to its square root is 20. So going by process of elimination, you can eliminate 5 because the square root of that is a decimal and 5 plus a decimal isn't going to add up to 20. You know you can eliminate 20 because it already reaches the limit with the number of tulips, not allowing enough room for daffodils. You can eliminate 4 because the square root of that is 2, and 4 + 2 = 6, not 20.
So that leaves 16... The square root of 16 is 4, because 4 divided by itself twice equals 16. Now, let's add them and see if it equals 20. 16 tulips + 4 daffodils = 20. So 16 is your answer.
Sorry I am bad at explaining things, but I hope this helps anyway!
Answer:
Option B is the correct answer.
Step-by-step explanation:
She used x tulips and some daffodils in the bouquet.
The number of daffodils is equal to the square root of the number of tulips.
[tex]\texttt{Number of daffodils = }\sqrt{x}[/tex]
The total number of flowers in the bouquet is 20
That is
[tex]x+\sqrt{x}=20[/tex]
Solving
[tex]x+\sqrt{x}=20\\\\\sqrt{x}=20-x\\\\x=(20-x)^2\\\\x=400-40x+x^2\\\\x^2-41x+400=0\\\\(x-25)(x-16)=0\\\\\texttt{x=25 or x = 16}[/tex]
Total number is less than 20 so 25 is not possible
Number of tulips used = 16
Option B is the correct answer.
Select the correct answer from the drop down menu
[tex](\frac{f}{g})(x)=\frac{x^{2} +2x-3}{x^2-9}[/tex] since x = 4, you plug in 4 into the x's in the equation
[tex](\frac{f}{g} )(4)=\frac{(4)^2+2(4)-3}{(4)^2-9} = \frac{16 + 8 - 3}{16 - 9}[/tex] Simplify
[tex]\frac{21}{7} =3[/tex]
so [tex](\frac{f}{g})(4)=3[/tex]
(f + g)(x) = (x² + 2x - 3) + (x² - 9) Plug in 4 for x
(f + g)(4) = 4² + 2(4) - 3 + (4)² - 9
(f + g)(4) = 16 + 8 - 3 + 16 - 9 = 28
The tables below show running hours of three printers that produce greeting cards and the total number of greeting cards produced over three weeks.
Number of Hours Machine Is Running
Printer A
Printer B
Printer C
Week 1
40
50
45
Week 2
45
50
40
Week 3
55
30
60
Total Cards Produced
Week 1
7,950
Week 2
7,800
Week 3
9,600
Printer B uses $15 in ink every hour. What is the ink cost for each card coming from printer B?
Answer:
$0.2456 / card in ink for printer B
Step-by-step explanation:
The formatting of the data tables isn't great in your question and it's hard to be sure of which numbers go where.
Since the question is about printer B, we'll assume the number of hours for printer B is 50 for week1, 50 for week2 and 3 for week3.
The numbers don't make much sense overall, but let's work with them.
We'll first calculate the ratio of hours worked by printer B with the overall hours all the printers worked, over the 3 weeks:
Printer A : 140 hours
Printer B : 130 hours
Printer C: 145 hours
Total 415 hours total, for the 3 printers.
Ratio of Printer B: 130 / 415 = 31.325%
Total of cards produced:
7,950 + 7,800 + 9,600 = 25,350 cards over 3 weeks.
We'll assume the productivity per hour is the same for all printers, since no indication otherwise. So, the portion of those 25K cards of printer B should be the same as the ratio of the hours worked:
25,340 * 31.325% = 7941 cards (rounded to the nearest unit)
Since we know printer B ran for 130 hours, and it costs $15/hour in ink, we have:
130 hours * 15$/hour = $1,950 in ink.
Now, we divide by the number of cards:
$1,950 / 7941 cards = $0.2456 / card in ink for printer B
Answer:
b
Step-by-step explanation:
took test
Quadratic relations help needed! Thank you
For this case we have that the distance between two points is:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2 (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) :( 3 \sqrt {7}, 2 \sqrt {5})\\(x_ {2}, y_ {2}) :( 5 \sqrt {7}, 5 \sqrt {5})[/tex]
Substituting:
[tex]d = \sqrt {(5 \sqrt {7} -3 \sqrt {7}) ^ 2+ (5 \sqrt {5} -2 \sqrt {5}) ^ 2}\\d = \sqrt {(2 \sqrt {7}) ^ 2+ (3 \sqrt {5}) ^ 2}\\d = \sqrt {4 (7) + 9 * (5)}\\d = \sqrt {28 + 45}\\d = \sqrt {73}\\d = 8.5440[/tex]
Answer:
[tex]d = 8.54[/tex]
h=64t-32t^2 find the maximum height attained by the obiect
Check the picture below.
so if we just find its vertex, we know how many feet it went up by its y-coordinate.
[tex]\bf h=64t-32t^2\implies h=-32t^2+64t+0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h=\stackrel{\stackrel{a}{\downarrow }}{-32}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{64}{2(-32)}~~,~~0-\cfrac{64^2}{4(-32)} \right)\implies \left( \stackrel{\stackrel{\textit{how many}}{\textit{seconds}}}{1}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{it went up}}}{32} \right)[/tex]
17.003 - 0.374 please show work
Answer:
16.629
Step-by-step explanation:
Start by setting up the numbers like the first picture. The borrow. To borrow we have to go the whole way over to the 7 since you can't borrow from 0. So the 7 becomes a 6 and the 0 becomes 10. Then the 10 becomes a 9 and the 0 becomes a 10. Then the 10 becomes a 9 and the 3 becomes a 13. Then subtract. Just bring the decimal point down.
y - 7x = 6
y +7x = 8
hence y is 7 ,x is 1/7
hope it helps you
17 out of 20 teens say they eat or drink something before school. if 3,000 students attend that highschool, predict the number of teenagers that eat or drink something before school PLZ HURRRRRRRRRRRYYYYYYYYYYYYY
Answer:
2,550
Step-by-step explanation:
3,000 divided by 20 equals 150.
17 multiplied by 150 equals 2,550.
the answer is 2,550 I agree
The probability for success of an event is P(A), and the probability of success of a second event is P(B). What is the
probability of both events occurring, in that order?
A.) P(A + B)
B.) P(A) . P(B)
C.) P(A) + P(B)
D.) P(A x B)
Answer:
b I am sure because to x the number to the the probability and we don't know which ]h one so there is a 50% 50% chance for both.
Step-by-step explanation:
Answer:
Option B - [tex]P(A)\cdot P(B)[/tex]
Step-by-step explanation:
Given : The probability for success of an event is P(A), and the probability of success of a second event is P(B).
To find : What is the probability of both events occurring, in that order?
Solution :
The probability for success of an event is P(A).
The probability of success of a second event is P(B).
As the events are independent so the probability of both events occurring, in that order is [tex]P(A)\cdot P(B)[/tex]
Therefore, Option C is correct.
The probability of both events occurring, in that order is [tex]P(A)\cdot P(B)[/tex]
Rewrite the function by completing the square. g(x)= x^2 + 15x +54
(24 POINTS)
The function can be written as g(x)=(x+15/2)^2 +(-9/4)
How to convert it?Some quadratic equations are difficult to factor and are not presented in a way that enables us to apply the square root property right away. However, by "completing the square," we may transform the quadratic formula into a perfect square trinomial. The square root property is then used to factor the trinomial and answer the equation.
How to Complete the Square in Equations to Solve the Problem
1. Transform the original equation into x2 + bx = c.
2. Add the term required to complete the square to both sides.
3. Factor the trinomial with a perfect square.
4. Apply the square root property to the resulting equation
If x2 + bx is a binomial, then adding will result in a perfect square trinomial. is the square of half the coefficient of the linear x.
A perfect square trinomial can be factored, so the equation can then be solved by taking the square root of both sides.
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Answer:
g(x)=(x+15/2)^2 +(-9/4)
Step-by-step explanation:
78 is 15% of what number
Answer:
520
Step-by-step explanation:
Is means equals and of means multiply
78 = 15% * W
Change to decimal form
78 = .15 *W
Divide by .15 on each side
78/.15 = .15W/.15
520 = W
Answer:
520
Step-by-step explanation:
78/0.15 = 520
tx²+3x-7=0 has two real solution. what can be the deducted about the value of t?
Answer:
value of t is greater than equal to -9 / 28.
Step-by-step explanation:
Given Quadratic Polynomial : tx² + 3x - 7 = 0
Also, It has real solutions.
Standard Quadratic equation, is ax² + bx + c = 0
here, Determinant, D = b² - 4ac
decides nature of the roots.
if D < 0 , roots / solutions are complex
if D = 0 , roots are real and equal.
if D > 0 , roots are real and different.
As given roots are real solutions.
Means Dis either equal to 0 or greater than 0
when D = 0
we have, 3² - 4 × t × (-7) = 0
9 + 28t = 0
t = -9 / 28
when D > 0
we have, 3² - 4 × t × (-7) > 0
9 + 28t > 0
t > -9 / 28
Therefore, value of t is greater than equal to -9 / 28.
Which data set is represented by the modified box plot? 116, 118, 114, 117, 151, 126, 122, 114, 124 100, 104, 114, 116, 117, 118, 122, 126, 151 116, 118, 104, 117, 151, 136, 142, 104, 124 106, 108, 104, 107, 151, 126, 132, 104, 124
100, 104, 114, 116, 117, 118, 122, 126, 151
That was the correct answer for the test I took