Answer:
The minimum sample size is [tex]n = 2123[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.028[/tex]
Given that the confidence level is 99% then the level of significance is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1 \%[/tex]
[tex]\alpha =0.01[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 2.58[/tex]
Now let assume that the sample proportion is [tex]\r p = 0.5[/tex]
hence [tex]\r q = 1 - \r p[/tex]
=> [tex]\r q = 0.50[/tex]
Generally the sample size is mathematically represented as
[tex]n =[ \frac{Z_{\frac{ \alpha }{2} }}{ E} ]^2 * \r p * \r q[/tex]
[tex]n =[ \frac{2.58}{ 0.028} ]^2 * 0.5 * 0.5[/tex]
[tex]n = 2123[/tex]
find the unknown angles
Answer:
y=135
x=45
Step-by-step explanation:
x= 45
It is an isosceles so
180-90=90
90/2= 45
y=135
angles on a straight line add up to 180 so
180-45=135
Hope this helps!
Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n
Answer:
The answer is option AStep-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 38
d = 32 - 38 = - 6 or 20 - 26 = - 6
Substitute the values into the above formula
A(n) = 38 + (n - 1)-6
= 38 - 6n + 6
We have the final answer as
A(n) = 44 - 6nHope this helps you
Answer:
a
Step-by-step explanation:
you're welcome!
Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = 5cos(t) ⇒ x / 5 = cos(t)
y = 2sin(t) ⇒ y / 2 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / 5 )² = cos²(t)
+ ( y / 2 )² = sin²(t)
_____________
x² / 25 + y² / 4 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
I need help with these
Answer:
2. 20 oranges
3. 18 yellow tulips
4. 23 students
What number is halfway between 250 and 300
Answer:
the number that is halfway between 250 and 300 is 275
Step-by-step explanation:
250+300= 550/2= 275
The number i,e halfway is 275.
Important information:The two numbers is 250 and 300.calculation:[tex]= (250 + 300) \div 2\\\\= 550 \div 2[/tex]
= 275
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Use a double angle identity to rewrite the formula r(Θ)=[tex]1/16v^2sin(theta)cos(theta)[/tex]
Answer:
1/32v²sin2θ
Step-by-step explanation:
Given the expression r(theta) = 1/16v²sinθcosθ
According to double angle of trigonometry identity;
Sin2θ = sin(θ+θ)
Sin2θ = sinθcosθ + cosθsinθ
Sin2θ = 2sinθcosθ
sinθcosθ = sin2θ/2 ... **
Substituting equation ** into the question
1/16v²sinθcosθ = 1/16v²(sin2θ/2)
1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)
1/16v²sinθcosθ = 1/32v²sin2θ
Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ
About 25% of young Americans have delayed starting a family due to the continued economic slump. Determine if the following statements are true or false, and explain your reasoning.a. The distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump in random samples of size 12 is right skewed.b. In order for the distribution of sample proportions of young Americans who have delayed starting a family due to the continued economic slump to be approximatly normal, we need random samples where the sample size is at least 40.c. A random sample of 50 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.d. A random sample of 150 young Americans where 20% have delayed starting a family due to the continued economic slump would be considered unusual.e. Tripling the sample size will reduce the standard error of the sample proportion by one-third.
Answer:
a. True
b. true
c. false
d. false
e. false
Step-by-step explanation:
a. true
polutation = 25% = 0.25
sample = n= 12
n x p
= 12 x o. 25 = 3 and 3 is less than 10
12(1 - p)
= 12 x 0.75
= 9 and is less than 10
b. True
the sample distribution of the population is normal when
sample size x population > or equal to 10
40 x 0.75
= 30 and 30 is greater than 10
c. false
50 x 0.25 = 12.5
50 x 0.20 = 10
z = 10 - 12.5/sqrt(12.5)
= -2.5/3.54
= -0.70
H0: Young american family who delayed
H1: young american family who did not delay
p(z = -0.70)
0.2420>0.005
therefore we accept the null hypothesis
d. false
150 x 0.20 = 30
150 x 0.75 = 37.5
z = 30 - 37.5/sqrt(37.5) = -7.5/6.12 = -1.22
p(z = -1.22) = 0.1112 > 0.05
therefore we do not reject the null hypothesis
e. false
se1 = sqrt(p(1-p)/n
se2 = sqrt(p(1-p)/3n
se2 = 1/sqrt(3)se2
A person collected $700 on a loan of $600 they made 5 years ago. If the person charged simple interest, what was the rate of interest? The interest rate is %. (Type an integer or decimal rounded to the nearest hundredth as needed.)
Answer:
Rate= 3 1/3%
Or Rate= 3.33%
Step-by-step explanation:
Final amount collected= $700
Initial amount given out= $600
Interest made= Final amount - initial amount
Interest made= $700-$600
Interest made= $100
Type of interest rate = simple
Number of years = 5
PRT/100= interest
R=(100*interest)/(PT)
R= (100*100)/(600*5)
R= 10000/3000
R= 10/3
R= 3 1/3%
Or R= 3.33%
Calculate the nominal rate of interest convertible once every four years that is equivalent to a nominal rate of discount convertible quarterly. Let d^(4) be the nominal rate of discount convertible quarterly.
Answer:
i am having issues using the math editor and my time is almost running out. i added an attachment.
Step-by-step explanation:
What does the tape measure say Measurement # 3 is? *
Answer:
5 and 3/32 of an inch.
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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What are the Links of two sides of a special right triangle with a 306090° and a Hypotenuse of 10
Answer:
Step-by-step explanation:
60°=2×30°
one angle is double the angle of the same right angled triangle.
so hypotenuse is double the smallest side.
Hypotenuse=10
smallest side=10/2=5
third side =√(10²-5²)=5√(2²-1)=5√3
A student wrote the following equation and solution. Explain the error and correctly solve the equation: √p = 9/16 p = 3/4
Answer:
see below
Step-by-step explanation:
√p = 9/16
We need to square each side, not take the square root
(√p)^2 =( 9/16)^2
p = 81/256
HELP PLEASE!! I have been working on this for about three hours!!
Answer:
see below
Step-by-step explanation:
First we need to find the slope
m = ( y2-y1)/ ( x2-x1)
= (60-64)/( 10-0)
= -6/10
= -2/5
The y intercept is (0,64)
The slope intercept form of the equation is
y = mx+b where m is the slope and b is the y intercept
y = -2/5 x + 64 where y is in the thousands of feet
m = -2/5 * 1000 = -400 ft / minute
The height decreases since the sign is negative
The height decreases 400 ft per minute
The y intercept is (0,64)
64 is in the thousands of ft
64*1000 = 64,000 ft
When it starts, it is at 64,000 ft
The descent starts at a cruising altitude of 64,000 ft
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[tex]\sf{\implies Range = Highest \: - lowest }[/tex]
→ Range of Lewistown = 74 - 64
→ Range of Lewistown = 10 .
→ Range of Hamersville = 71 - 55
→ Range of Hamersville = 16 .
☆ Range of Hamersville - Range of Lewistown
→ 16 - 10
→ 6
Answer → The range for Hamersville is 6 more than the range for Lewistown .
PLEASE HELP ME WITH THIS QUESTION
Answer:
y-k
x-h
Step-by-step explanation:
Given E &D, F would be at (x, k).
That means E to F would be y-k.
And F to D would be x-h.
I assume you don’t need to find E to D, since that’s just r. (You could use the Distance Formula or Pythagoreans theorem to come up with and equation, but it wouldn‘t be one of those listed.)
Can someone help me, please?
Answer:
16
Step-by-step explanation:
7x+20+2x-5=159
9x+15=159
9x=159-15
9x=144
x=16
CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness df the cake, since
this will be the same, regardless of its diameter.)
10.1
in
Answer:
15.7 in
Step-by-step explanation:
A slice of a round pie is a sector of a circle.
The perimeter of a slice is the arc length s plus twice the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. So,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 in
The diameter of the cake should be 15.7 in.
Check:
[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]
It checks.
(4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000 (c) x 3 100 − 1000x 2 (d) x log x (2) (2 points) U
Answer:
(a) O(x²)
(b) O(x²)
(c) O(x²)
(d) Not O(x²)
Step-by-step explanation:
If a function is O(x²), then the highest power of x in the function ia greater or equal to 2.
(a) 100x + 1000
This is O(x), not O(x²)
(b) 100x² + 1000
This is O(x²)
(c) x³.100 − 1000x²
This is O(x²)
(d) x log x²
This is not O(x²)
In a lottery game, a player picks 6 numbers from 1 to 50. If 5 of the 6 numbers match those drawn, the player wins second prize. What is the probability of winning this prize
Answer:
1/254,251,200 Or 0.000000003933118
Step-by-step explanation:
1/50x1/49x1/48x1/47x1/46=1/254,251,200
what is the least number to be added to 1500 to make it a perfect square?
Answer:
21
Step-by-step explanation:
√1500 ≈ 38.7
round that up to 39 and square it:
39² = 1521
Help me solve this!!!
Answer:
54°
Step-by-step explanation:
Let ∠CYX=x
AB║CD
∠AXE=∠CYX (corresponding angles)
∠AXE=3∠CYX-108
x=3x-108
3x-x=108
2x=108
x=108/2=54°
∠AXE=∠CYX=x=54°
∠BXY=∠AXE=54° (Vertically opposite angles)
For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer: 0.81
Step-by-step explanation:
[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]
There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?
Answer:
97290
Step-by-step explanation:
47 different people can win first
47
Now there are only 46 people left
46 different people can win second
46
45 different people can win third
47*46*45
97290
An amusement park is open 7 days a week. The park has 8 ticket booths, and each booth has a ticket seller from 10am to 6pm. On average, ticket sellers work 30 hours per week. Write and equation that can be used to find "t", the minimum number of ticket sellers the park needs. show work if possible.
Answer:
t = (448 hrs/ week) / (30 hrs / week)
Step-by-step explanation:
Number of times park opens in a week = 7
Number of ticket booth = 8
Opening hours = 10am - 6pm = 8 hours per day
Max working hours per ticket seller per week = 30 hours
Therefore each booth works for 8 hours per day,
Then ( 8 * 7) = 56 hours per week.
All 8 booths work for (56 * 8) = 448 hours per week
If Max working hours per ticket seller per week = 30 hours,
Then muninim number of workers required (t) :
Total working hours of all booth / maximum number of working hours per worker per week
t = (448 hrs/ week) / (30 hrs / week)
Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 400 and the product is a maximum.
Answer:
100 and 200Step-by-step explanation:
Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;
a+2b = 400 ....
From the equation above, a = 400 - 2b ... 2
If the product of the numbers is a maximum then;
ab = (400-2b)b
let f(b) be the product of the function.
f(b) = (400-2b)b
f(b) = 400b-2b²
For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0
f'(b)= 400-4b = 0
400-4b = 0
400 = 4b
b = 400/4
b = 100
Substituting b= 100 into the equation a = 400 - 2b to get a;
a = 400 - 2(100)
a = 400 - 200
a = 200
The two positive integers are 100 and 200.
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
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1. Quadratics: The path of the longest shot put by the Women’s track team at Sun Devil U is modeledby h(x) = -0.015x2 + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) isthe height of the shot put above the ground. (Both x and h(x) are measured in feet.)a. [3 pts] Determine h(24). Round your answer to 2 decimal places.
Answer:
23.08 feetStep-by-step explanation:
If the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;
[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]
Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.
Jill works at a cell phone store. Jill earns $175 every week plus $45 for every phone p that she sells. if Jill makes $445 at the end of the week how many phones did she sell?
━━━━━━━☆☆━━━━━━━
▹ Answer
6 phones
▹ Step-by-Step Explanation
$445 - $175 = $270
$270 ÷ $45 = 6
6 phones
Hope this helps!
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━━━━━━━☆☆━━━━━━━
A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points
Answer: Option B, 16/81
Step-by-step explanation:
So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.
We know that every integer number can be "decomposed" into a product of prime numbers.
Then a number N, that is divisible by 3, can be written as:
N = 3*k
Where k is another integer.
Here we will have a product of 4 numbers, each of them are in between 1 and 6.
Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2
Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.
Then we must have a 1, 2, 4 or 5.
The probability of 4 outcomes out of 6, is:
P = 4/6.
But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:
P = (4/6)^4 = (2/3)^4 = 16/81
Answer:
16
Step-by-step explanation:
