Answer:
A sample of 139 should be taken.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Population standard deviation of $3,000.
This means that [tex]\sigma = 3000[/tex]
How large a sample should be taken if the desired margin of error is $500?
A sample of n is needed.
n is found when M = 500. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]500 = 1.96\frac{3000}{\sqrt{n}}[/tex]
[tex]500\sqrt{n} = 1.96*3000[/tex]
Dividing both sides by 500
[tex]\sqrt{n} = 1.96*6[/tex]
[tex](\sqrt{n})^2 = (1.96*6)^2[/tex]
[tex]n = 138.3[/tex]
Rounding up:
A sample of 139 should be taken.
What is the order of the following set of numbers from greatest to least? 1 1/3, 2/3, -1/3. 9/5 O 1/3,2/3,9/5, 1 1/3 -1/3.1 1/3, 2/3, 9/5 09/5, 2/3,1 1/3,-1/3 9/5, 1 1/3, 2/3, -1/3
Answer:
11/3, 9/5, 9/5 , 2/3 , 1/3 , -1/3.1 , -1/3
find the value of x in the triangle shown below 9 and 8 and x
Answer:
x=5.8
Step-by-step explanation:
I kinda guessed on this due to the fact you didn't provide a photo. I used the pythagorean equation to solve this.
Start by identifying you a, b, and c sides.
13. What is the perimeter of the triangle below?
X+14 X+14 2x+36
Answer:
4x + 64
Step-by-step explanation:
(X + 14) + (X + 14) + (2x + 36) = 4x + 64
ANSWER THE QUESTION FOR BRAINLIEST
A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that: (a) Fewer than 14 of them have had a physical examination in the past two years. (b) At least 17 of them have had a physical exami- nation in the past two years
Answer:
a) 0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.
b) 0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.
Step-by-step explanation:
For each women, there are only two possible outcomes. Either they visit their doctors for a physical examination at least once in two years, or they do not. The probability of a woman visiting their doctor at least once in this period is independent of any other women. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
70% of adult women visit their doctors for a physical examination at least once in two years.
This means that [tex]p = 0.7[/tex]
20 adult women
This means that [tex]n = 20[/tex]
(a) Fewer than 14 of them have had a physical examination in the past two years.
This is:
[tex]P(X < 14) = 1 - P(X \geq 14)[/tex]
In which
[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 14) = C_{20,14}.(0.7)^{14}.(0.3)^{6} = 0.1916[/tex]
[tex]P(X = 15) = C_{20,15}.(0.7)^{15}.(0.3)^{5} = 0.1789[/tex]
[tex]P(X = 16) = C_{20,16}.(0.7)^{16}.(0.3)^{4} = 0.1304[/tex]
[tex]P(X = 17) = C_{20,14}.(0.7)^{17}.(0.3)^{3} = 0.0716[/tex]
[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]
[tex]P(X = 19) = C_{20,19}.(0.7)^{19}.(0.3)^{1} = 0.0068[/tex]
[tex]P(X = 20) = C_{20,20}.(0.7)^{20}.(0.3)^{0} = 0.0008[/tex]
So
[tex]P(X \geq 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1916 + 0.1789 + 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.6079[/tex]
[tex]P(X < 14) = 1 - P(X \geq 14) = 1 - 0.6079 = 0.3921[/tex]
0.3921 = 39.21% probability that fewer than 14 of them have had a physical examination in the past two years.
(b) At least 17 of them have had a physical examination in the past two years
[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)[/tex]
From the values found in item (a).
[tex]P(X \geq 17) = P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.107[/tex]
0.107 = 10.7% probability that at least 17 of them have had a physical examination in the past two years.
A town has a population of 20,000 and grows at 4.5% every year how long will it be in to the population is 42,800
Answer:
It will take 17 years to get a population of 42,800. (Specifically 17.3)
Step-by-step explanation:
We will use the equation
y = population
x = amount of years
y = 20000(1 + 0.045)^x
20000 is the original population.
(1 + 0.045) is the increase of 4.5% every year
What is the difference in volume between a sphere with radius r and a sphere with radius 0.3r?
Answer:
[tex]d = 1.2973\pi r^3[/tex]
Step-by-step explanation:
Given
[tex]R_1 = r[/tex]
[tex]R_2 = 0.3[/tex]
Required
The difference in their volumes
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
So, the difference d is:
[tex]d = \frac{4}{3}\pi [R_1^3 - R_2^3][/tex]
[tex]d = \frac{4}{3}\pi [r^3 - (0.3r)^3][/tex]
[tex]d = \frac{4}{3}\pi [r^3 - 0.027r^3][/tex]
[tex]d = \frac{4}{3}\pi *0.973r^3[/tex]
[tex]d = \frac{3.892}{3}\pi r^3[/tex]
[tex]d = 1.2973\pi r^3[/tex]
Volume is a three-dimensional scalar quantity. The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the sphere with radius(r) is,
Volume = (4/3)×π×r³
The volume of the sphere with radius (0.3r) is,
Volume = (4/3)×π×(0.3r)³
The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is,
Difference = [(4/3)×π×r³] - [(4/3)×π×(0.3r)³]
= (4/3)πr³[1-0.027]
= (4/3)πr³(0.973)
= 4.0757r³ unit³
Hence, The difference in the volume between a sphere with radius r and a sphere with radius 0.3r is 4.0757r³ unit³.
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the ratio of boy to girls in a school 1s 5:7. if there are 780 students in the school, how many boys are in the school?
Answer:
325 boys
Step-by-step explanation:
The ratio 5:7 represents 5+7=12 students. If we were to proportionalize this ratio to 780 students, we would multiply the ratio by 65/65 since 780/12=65.
Therefore, you have (5*65)/(7*65)=325/455 as your ratio. This means that there are 325 boys in the school
The sum of two numbers is 7 and the difference of their squares is 105. Find the numbers. If there
In simplest form.
more than one pair, use the "or" button. Give the answer
In simplest form
Answer:
11 and -4
Step-by-step explanation:
Let the required two numbers be x and y
If the sum of two numbers is 7, then
x + y = 7 .. 1
If the difference of their squares is 105, then;
x² - y² = 105 ...2
From 1;
x = 7 - y... 3
Substitute 3 into 2;
(7-y)² - y² = 105
Expand
49-14y+y² -y² = 105
49-14y = 105
-14y = 105 - 49
-14y = 56
y = -56/14
y = -4
Substitute y = -4 into 3
x = 7 - y... 3
x = 7 - (-4)
x = 7+4
x = 11
Hence the numbers are 11 and -4
4 1/8 take away 1 1/2 mixed numbers
Answer:
21/8 or 2 3/8
Step-by-step explanation:
33/8 - 3/2
33/8 - 12/8=21/8
hope it helps:)
What is the measure of angel C?
Enter your answer as a decimal. Round only your final answer to the nearest hundredth.
m
Answer:
36.87
Step-by-step explanation:
We can use SOH CAH TOA (sine, cosine, and tangent) to solve this problem.
SOH- means Opposite over Hypotenuse
CAH- means Adjacent over Hypotenuse
TOA- mean Opposite over Adjacent
U can use either one of these to solve this problem, I will be using sine SOH (sine).
sine C = 3/5
sine ^-1 3 divided by 5 =36.8698
So, angle C = 36.8698 and rounded to the nearest hundred is 36.87
Amanda runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?
Answer:
5.6 miles
Step-by-step explanation:
[tex]\frac{7}{80} =\frac{x}{64}[/tex] Set up the proportion
[tex]7(64)=x(80)[/tex] Cross multiply
[tex]448=80x[/tex] Simplify
[tex]\frac{448}{80}=\frac{80x}{80}[/tex] Divide both sides by 80
[tex]5.6=x[/tex]
Write 44/5 as a mixed/whole number.
Write 12/3 as a mixed/whole number.
Write 5/5 as a mixed/whole number.
Write 15/7 as a mixed/whole number.
Write 1/4 as a mixed/whole number.
Answer:
12/3=4
5/5=7
15/7=2+1/7
1/4 is a proper fraction
Only improper fractions can be converted to mixed/whole number
Step-by-step explanation:
Help on this math question. 25 points.
Answer:
the third one
Step-by-step explanation:
Find an equation of the circle having the given center and radius.
Center (-7, 6), radius 6
Answer:
36 = (x+7)^2 + (y-6)^2
Step-by-step explanation:
6^2=(x-(-7))^2 + (y-6)^2
For which of the inequalities below is v = 4 a solution?
v plus greater 8
v plus 5 greater or equal than 9
v plus 5 greater than 9
v plus 5 less or equal than 8
Answer:
Option 2, v plus 5 greater or equal than 9
Step-by-step explanation:
For inequality represented by option 2 i.e v plus 5 greater or equal than 9
v+5 >= 9
If we put v =4 in above inequality, we get
4+5>= 9
9>= 9
Hence, option 2 is correct
Answer:
Option 2
Step-by-step explanation:
I need help please? :(
Answer:
C
Step-by-step explanation:
help. this is my daughter's math. how does it work?
Answer:
An ion with a -2 charge, atomic number 17, an atomic mass of 25 has how many electrons?
Step-by-step explanation:
Help me
Which of the points (s, t) is not one of the vertices of the shaded region of the
set of inequalities shown below?
ss 20 -0.5t
s 12-t
ss 24-t
S>O
t>0
Answer:
24,0
Step-by-step explanation:
which of the following numbers is a prime number greater than 23?
a)17 b)24 c)25 d)29 please no links
Find the area of the following figure with the given dimension.
Answer: 54 cm^2
Step-by-step explanation:
Area of a triangle= 1/2 * b * h
A= 1/2 * 9 * 12
A= (9*12)/2
A= 108/2
A- 54 cm^2
Maria wants to spend less than $110. She wants to buy some shirts, s.
that are priced at $9 each. She also decided to buy a pair of high heels for
$60. WRITE THE INEQUALITY that represents the word problem to
determine the number of shirts she can buy.
she can buy 5 shirts
Ms. Jaffey had a total of 428.5 ounces of pretzels to put into 5 bowls for a party. She put an equal number of ounces of pretzels into each bowl. How many ounces of pretzels did Ms. Jaffey put into each bowl?
Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.
To find out how many ounces of pretzels Ms. Jaffey put into each bowl, we need to divide the total number of ounces by the number of bowls.
Ms. Jaffey had a total of 428.5 ounces of pretzels, and she distributed them equally among 5 bowls. Therefore, we can divide the total number of ounces by 5 to determine the amount in each bowl.
428.5 ounces ÷ 5 bowls = 85.7 ounces.
So, Ms. Jaffey put approximately 85.7 ounces of pretzels into each bowl.
Since it's unlikely to have exact measurements when dividing a total quantity into equal parts, we round the result to one decimal place, giving us 85.7 ounces. This means that each bowl contains approximately 85.7 ounces of pretzels.
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Please help, test due in 1 hour! I will give brainliest!
Item 1
The table gives estimated annual salaries associated with two levels of education.
Level of education High school diploma Trade school certification
Estimated annual salary $27,500 $48,000
Based on the table, how much more money would a person with a trade school certification earn than a person with a high school diploma over a 30 year career?
$20,500
$75,500
$82,500
$615,000
Answer:A) 20,500
Step-by-step explanation: because 27,000+48,00=75,00 so you divdie that by 30 and you will get your answer of 20,500
help please, asap. i need this done
Answer:
30
Step-by-step explanation:
24/4=6
42/7=6
6 x 5=30
The angle \theta_1θ
1
theta, start subscript, 1, end subscript is located in Quadrant \text{II}IIstart text, I, I, end text, and \sin(\theta_1)=\dfrac{9}{41}sin(θ
1
)=
41
9
sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 9, divided by, 41, end fraction .
What is the value of \cos(\theta_1)cos(θ
1
)cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Trig identity are written in term of cosine, sine and tangent, he value of cosθ if the value of sinθ is 9/41 is 40/41
Trigonometry ratioGiven the following parameters
sinθ = 9/41
According to the SOH CAH TOA identity
sinθ = opposite/hypotenuse
Determine the adjacent sides
a= √41² - 9²
a = √ 1600
a = 40
Determine the value of cosθ
cosθ = adjacent/hypotenuse
cosθ = 40/41
Hence the value of cosθ if the value of sinθ is 9/41 is 40/41
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Answer:
-40/41
Step-by-step explanation:
Find the quotient of 5 ÷ 1 8 .
A.5/8
B.8/5
C.4
D.40
5÷18
answer D 40 quotient
The angles below are complementary. Find the value of X
Regina writes the expression y+9 ∙ 34. Which expression is equivalent to the one Regina writes?
None of these
(9 ∙ 3÷4)+y
(y+9)(3÷4)
9+y ∙(3÷4)
