For any confidence level C, the value of the sample proportion will always be considered a plausible value for p is a true statement.
For any given confidence level, the sample proportion of a given sample will always be within the range of values that are considered plausible for the population proportion. This range is determined by the confidence interval, which is calculated based on the confidence level C. Thus, the sample proportion will always be considered a plausible value for p.
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What's the sum of ⅜ and ¼6?
O A. ½4
О B.¼
О C.⅙
O D. ¼6
Step-by-step explanation:
Very simple… first convert everything to the same denominator…
1/8 + 2/8 + 3/8… Add the numerators together, and you get 6/8.
Simplify 6/8 to its lowest form… and your answer is ⅙ !
Pre cal NEED HELP PLEASE!
========================================================
Explanation:
Let point C represent the center of the planet.
Segment QC is 2810 miles long as it's one of the radii.
Segment DC is 1970+2810 = 4780 miles long after adding on the height of the mountain.
Triangle DQC is a right triangle. That allows us to use a trig ratio to determine theta. Specifically we'll use cosine.
cos(angle) = adjacent/hypotenuse
cos(theta) = QC/DC
cos(theta) = 2810/4780
theta = arccos(2810/4780)
theta = 53.9942734 degrees approximately
A full 360 degree rotation takes 24 hours. We take a fraction of that to find how many hours it takes for that planet to rotate so point P ends up where point Q is currently located.
(theta/360)*24 = (53.9942734/360)*24 = 3.599618
That's the number of approximate hours it takes. Multiply that by 60 to determine how many minutes it takes.
3.599618*60 = 215.97708
Then that rounds to the final answer 215.98 minutes.
A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function S
(
t
)
=
37
+
16
e
−
0.04
t
, where t
is the time (in years) since the stock was purchased. Find the average price of the stock over the first eight years.
The average price of the stock over the first eight years is 50.69 units / year .
Given :
A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function :
S ( t ) = 37 + 16 e^0.04t.
We find the average value of the stock ,
[tex]f_{ave} =1/b-a \int\limits^8_0 {f(x)} \, dx[/tex]
[tex]f_{ave} =1/8-0 \int\limits^8_0 {S (t)} \, dx[/tex]
[tex]f_{ave} =1/8( \int\limits^8_0 {37} \, dt + \int\limits^8_0 {16e^{(0.04t) \, dt[/tex]
= 37 / 8 ( 8 - 0 ) - 1 / 0.02 ( [tex]e^{-0.04 * 8 }[/tex] - [tex]e^{-0.04 * 0[/tex])
= 50.69 units / year.
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What is the greatest common factor of the following numbers? 16, 24, 32, 40 A. 4 B. 8 C 2 D. 16
Answer:
b
Step-by-step explanation:
The factors of 16 are: 1, 2, 4, 8, 16
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40
Then the greatest common factor is 8
Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at end of the 12th year, the company invests $8,000 at end of each year at 5% compounded annually. The amount of the original loan was
Multiple Choice
$127,337.01
$70,905.60
$127,636.80
$70,950.60
The required future value of the annuity is $127,336.80.
Jones Company borrowed money that must be paid back in 12 years. To ensure that the debt is repaid by the end of the 12th year, the corporation invests $8,000 at the end of each year at a rate of 5% compounded yearly.
Compute the future value of the annuity as follows:
Future value = Annuity - FVIFA
FVIFA is taken from the table, and substitutes the value of the annuity in the above formula
Future value = $8,000 × 15.9171
Apply the multiplication operation, and we get
Future value = $127,336.80
Therefore, the required future value of the annuity is $127,336.80.
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The graph of y = f(x) is shown below. Find all values of a where
f(x) = 6
Step-by-step explanation:
where is graph?....can u upload graph pic too?
Tanya has a collection of 52 rocks that she wants to put into display cases. Each display case can hold 8 rocks. Tanya divides to find how many cases
she needs.
52÷8=614
How many display cases will Tanya need?
A. 4
B. 6
C. 7
D. 8
E. 10
find the solution to the system of equations
Answer:
Step-by-step explanation:
Find the corner points of X (x,y) and Y(x,y)
Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true? a) A = BUC b) B is a singleton set. c) A = CU{2} d) All of the mentioned
After analyzing the given data we will get to know that all the options mentioned above are true.
A = BUC, B is a singleton set, and A = CU2 if A is the set of all prime numbers, B is the set of all even prime numbers, and C is the set of all odd prime numbers. Therefore, option D - All of the specified - is the answer to this question.
We've got
The entire set of prime numbers is A.
A = {2, 3, 5, 7, 11, 13}
B is a collection of even prime numbers.
B = {2}
C is a collection of all odd prime numbers.
C = {3, 5, 7, 11, 13,}
We are aware that the only even prime number is two. As a result, Set B is a singleton set because it only has one element.
Additionally, if we combine sets B and C, we will obtain set A, which contains all prime numbers.
Thus, we obtain A = B U C.
Since B = 2 is a singleton set, if we have A = B U C, we can also say A = C U 2.
Therefore, each of the aforementioned choices is appropriate.
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In a class of students, the following data table
summarizes how many
students have a brother or a sister. What is the probability that a student
chosen randomly from the class has a sister?
Has: brother Does not have a brother
Has a sister
6
12
Does not have a sister
3
The probability that a student chosen randomly from the class has a sister is 3/5.
What is the probability of an event?The probability of an event is the fraction of the number of favorable occurrences of an event to the total occurrences of the event.
P(a) = n(a)/n(s)
where 'a' is an event.
Calculation:The given data table shows how many students have a brother or a sister in a class of students.
The number of students who have both a sister and a brother = 6
The number of students who have only a brother and do not have a sister = 3
The number of students who have only a sister and do not have a brother = 12
The number of students who do not have both a sister and a brother = 9
So, the total number of students in the class = 6 + 3 + 12 + 9 = 30
Then, the probability that a student chosen randomly from te class has a sister is
= (number of students who have a sister)/total number of students
= (6 + 12)/30
= 18/30
= 3/5
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Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is):
Multiple Choice
$1,350
$1,535.21
$1,653
$5,163
The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).
Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.
Assuming a semiannual compounding rate of 8%,
As per the given information, the required solution would be as:
Amount to be paid into the fund each semi-annual period will be
= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))
= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))
= $1535.21
Thus, the required amount to be paid into the fund each period is $1535.21.
Hence, the correct answer would be an option (B).
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the exponential model a=368.3e ^0.002t describes the population, a, of a country in millions, t years after 2003. use the model to determine the population of the country in 2003
the population of the country in 2003 is, 368.3 million.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
The population's description is provided by the exponential model a = 368.3e0.002t.
"a" denotes a nation's population in millions,
following 2003 by t years.
We must ascertain the country's population in 2003.
At 2003, t = 0.
In the exponential model above, enter t = 0.
a = 368.3e^0.002(0) (0)
a = 368.3e^0
a = 368.3
Hence, the population of the country in 2003 is, 368.3 million.
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Which function could be represented by this graph
Answer:
The function is going up
Step-by-step explanation:
the arrow is going up
Answer: y=2^{x}
Step-by-step explanation:
Value of x on 10x+12=2
Answer:
[tex]x = -1[/tex]
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Addition
Subtraction
~
First, subtract 12 from both sides of the equation:
[tex]10x + 12 = 2\\10x + 12 (-12) = 2 (-12)\\10x = 2 - 12\\10x = -10[/tex]
Next, divide 10 from both sides of the equation:
[tex]10x = -10\\\frac{(10x)}{10} = -\frac{(10)}{10}\\ x = -\frac{10}{10} = -1\\ x = -1[/tex]
[tex]\textbf {x = -1}[/tex] is your answer.
~
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A rectangular paperboard measuring 20 in long and 12 in wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer
The area of the remaining paperboard is 246.91 in²
How to we calculate cut out area?A shape can be cut-out of another shape. For example a circle cut off a rectangle. The area of the remaining part of the shape can be calculated as area of original shape - area of cut-out shape
The area of a rectangle = l×w
= 20×21 = 420in²
a semi circle is the shape cut-out, therefore the area of the semi circle= ½πr²
= ½×3.14× 10.5²= 173.09in²
Therefore the area of the remaining part of the paperboard is 420-173.09= 246.91 in²
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The UGA Journalism Department is interesting in determining if there is a significant difference in the number of hours, on average per week, that UGA males and UGA female students spend reading any online or printed newspaper. Randomly selected students at UGA were asked how many hours per week they read any online or printed newspaper, their age, and gender. The 95% confidence interval for reading newspapers on μF-urn is (-1.1, 1.3). 1) Interpret this confidence interval. Because 0 is not in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is not in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males. Because 0 is in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
The option C, “because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males” is correct.
In the given question, the UGA Journalism Department is interesting in determining if there is a significant difference in the number of hours, on average per week, that UGA males and UGA female students spend reading any online or printed newspaper.
Randomly selected students at UGA were asked how many hours per week they read any online or printed newspaper, their age, and gender. The 95% confidence interval for reading newspapers on μ(F)-μ(M) is (-1.1, 1.3).
1) We have to interpret this confidence interval. The given options are:
• Because 0 is not in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is not in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males.
• Because 0 is in this interval, we can conclude that there is a difference in newspaper reading, on average, for females and males.
Since there interval was given.
The given interval for the 95% confidence interval for reading newspapers on μ(F)-μ(M) is (-1.1, 1.3).
Since the value of interval is between -1.1 and 1.3. So 0 is in this interval. So we cannot conclude that there is a difference in newspaper reading, on average, for females and male.
So the option C, “because 0 is in this interval, we cannot conclude that there is a difference in newspaper reading, on average, for females and males” is correct.
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Which of the following is √ 48 simplified?
Answer:
4√3
Step-by-step explanation:
√48
If we factor it out we will get
√4^2 ⋅ 3
Then we pull terms out from under the radical
4√3
So, the answer is 4√3
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Given the vector u equal to 7 (cos 330°, sin 330°) and vector v equal to
4 (cos 90º, sin 90°), find the sum u + v and write your answer in magnitude and
direction form with the magnitude rounded to the nearest tenth and the direction
rounded to the nearest degree, 0° ≤ 0 < 360°.
The magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree 5.4<cos335°<, sin335°
What is direction ?
Direction is characterized as the course that anything follows, the route that must be taken to go to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.
The basis of the x, y, and z directions of a line or unit vector is identified by the number triplet known as the direction number. They are easily identified as a percentage of a unit vector.
u = 7cos300°i + 7sin300j
v = 4cos70i + 4sin70 j
u = 7*0.5i + 7*(-√3/2)j
= 3.5i - 6.062j
v = 1.368i + 3.758j
u + v =(3.5+1.368)i +(-6.062+3.758)j
= 4.868i +(-2.304)j
Magnitude of (u+v) = √(4.868)² +(2.304)²
= 5.385 ≈ 5.4
For direction
tanФ = y/x
= -2.304/4.868
Ф = -25.327
∴(u+v) is in 4th Quandrant
∴ Ф = 360 - 25.327
= 334.672
≈ 335°
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A pair of dice is thrown and the sum of the two scores is calculated. What’s the expected value of the roll?
A. 5
B. 6
C. 7
D. 8
A pair of dice is thrown the sum of the 2 scores calculated can be 5,6,7,8
How do you calculate probability?The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
What are the 3 types of probability?The Three Kinds of Probability
Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).
Subjective Probability. Definition of Relative Frequency.
The value of dice is 1,2,3,4,5,6
Hence the sum of the 2 dice when rolled together can vary from 2 to 12
since 5,6,7,8 lies between 2 and 12
all of them are correct.
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Test the claim that for the population of statistics final exams, the mean score is 71 using alternative hypothesis that the mean score is different from 71. Sample statistics include n = 26, ã = 72, and s = 18. Use a significance level of a = 0.05. (Assume x : normally distributed population.) = a a The test statistic is 0.283 The positive critical value is 1.645 The negative critical value is 1.645
Since the test statistic is not greater than the critical value, the null hypothesis cannot be rejected. Therefore, the claim that the mean score is 71 is not rejected.
1. We are given the population of statistics final exams and asked to test the claim that the mean score is 71 using an alternative hypothesis that the mean score is different from 71. We are also given the sample statistics including the sample size (n = 26), the sample mean (ã = 72), and the sample standard deviation (s = 18). We are asked to use a significance level of α = 0.05.
2. Since we are assuming that the population is normally distributed, we will use a two-tailed z-test to test the claim.
3. The null hypothesis is that the mean score is 71 and the alternative hypothesis is that the mean score is different from 71.
4. The test statistic is calculated as:
Test statistic = (sample mean - population mean) / (standard deviation/√n)
= (72 - 71) / (18/√26)
= 0.283
5. The critical values for a two-tailed z-test with a significance level of α = 0.05 are 1.645 for both the positive and negative critical values.
6. Since the test statistic (0.283) is not greater than the critical value
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Which of the following correctly describes the steps to find the volume of a cylinder?
A. Find the circumference of the base and multiply it by the height of the cylinder.
B. Find the area of the base and multiply it by the height of the cylinder.
C. Square the area of the base and multiply it by the height of the cylinder.
D. Find the area of the base and add it to the height of the cylinder.
Answer:
B. Find the area of the base and multiply it by the height of the cylinder.
Step-by-step explanation:
πr^2h is the formula for finding the volume of a cylinder.
You find the area of the base by squaring the radius, then do pi times base area times height to get the volume.
Find the dimensions of the rectangle with the greatest area that can be built so the base of the rectangle is on the x-axis between 0 and 1 (0 less than equal to x less than equal to 1) and one corner of the rectangle is on the curve, y = x^3 . What is the area of this rectangle?
The area of this rectangle is 0.105C that can be calculated by implementing the dimensions of length and breadth.
The area of rectangle involves the length and breadth.
Suppose length of rectangle be a,
Height of rectangle (1-a)^3
Area, A= a*(1-a)^3
dA/da = -3a(1-a)^2+(1-a)^3 = 0
a = 1, 0.25
Thus, Area (max) = 0.25*0.75^3 = 0.105
In this case
Height of rectangle C(1-a)^3
Area, A= Ca*(1-a)^3
dA/da = C[-3a(1-a)^2+(1-a)^3] = 0
a = 1, 0.25
Thus, Area (max) = 0.25*0.75^3*C = 0.105C
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if 4 apple pies require 22 apples, how many pies can be made with 77 apples?
Answer:
14
Step By Step
22/4= 5.5 77/5.5= 14
the standard iq test is designed so that the mean is and the standard deviation is for the population of all adults. we wish to find the sample size necessary to estimate the mean iq score of statistics students. suppose we want to be % confident that our sample mean is within iq points of the true mean. the mean for this population is clearly greater than . the standard deviation for this population is probably less than because it is a group with less variation than a group randomly selected from the general population; therefore, if we use we are being conservative by using a value that will make the sample size at least as large as necessary. assume then that and determine the required sample size.
If we assume that σ = 15 then the required sample size is 216 .
In the question ,
it is given that ,
the standard deviation is (σ) = 15
we want to be 95% confident . So , α [tex]=[/tex] 1 - 0.95 = 0.05
So , [tex]Z_{\frac{\alpha }{2} }[/tex] is = [tex]Z_{\frac{0.05 }{2} }[/tex] = Z₀.₀₂₅
from z table ,
Z₀.₀₂₅ = 1.96 .
e is given to be = 2 IQ points
the sample size (n) is calculated using the formula .
n = (σ × [tex]Z_{\frac{\alpha }{2} }[/tex]/e)²
Substituting the values ,
we get ,
n = (15 * 1.96/2)²
n = (29.4/2)²
n = (14.7)²
n = 216.09
n ≈ 216
Therefore , the sample size necessary to estimate the mean IQ score of statistics students is 216 .
The given question is incomplete , the complete question is
The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of statistics students. Suppose we want to be 90% confident that our sample mean is within 2 IQ points of the true mean. Assume then that σ = 15 and determine the required sample size .
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Johnny has 121 apples, Johnny buys 3 apples from David 61 times. How many apples does Johnny have now?
Answer: 304
Step-by-step explanation: Johnny starts with 121 apples. He then buys 3 apples from david 61 times. (3x61) 183+121 =304
2. Mateo graphs quadrilateral EFGH and then reflects it across the
line y = 2. How are the x-coordinates of corresponding points in
the image and the preimage related?
After reflecting the quadrilateral EFGH across the line y = 2, the x-coordinates of the corresponding points in the image and the preimage will be the same.
What is Reflection?Generally, Reflection is an isometry, which means that it preserves distance and angles. Therefore, the x-coordinates of the points in the image and the preimage will not be changed by the reflection. The y-coordinates will change since the reflection flips the points over the line of reflection.
For example, if quadrilateral EFGH has a vertex at (x, y), then the corresponding vertex in the image will be at (x, 2 - y). The x-coordinate remains the same, but the y-coordinate is reflected across the line y = 2.
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185
+50%+4%=start fraction, 185, divided by, 100, end fraction, plus, 50, percent, plus, 4, percent, equals
Answer:
1.85
Step-by-step explanation:
185/100 equals 1.85
if I'm reading the problem correctly this is what we have:
0.54 = 1.85 + 0.54
for the left side to equal the right side you must add 1.85 or 185/100
See attached for the question
Check the picture below.
Answer:
∠ U = 12°
Step-by-step explanation:
the inscribed angle RST is half the measure of its intercepted arc RT , then
arc RT = 2 × ∠ RST = 2 × 30° = 60°
the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is
∠ U = [tex]\frac{1}{2}[/tex] ( RS - RT ) = [tex]\frac{1}{2}[/tex] × (84 - 60)° = [tex]\frac{1}{2}[/tex] × 24° = 12°
Part 1 of 2
Describe and correct the error a student
made finding the intercepts of the graph
of the line 4x-6y = 12.
1.4(0)-6y = 12
2. 6y=12, so y = 2; the y-intercept is 2.
3.4x-6(0) = 12
4.4x = 12, so x = 3; the x-intercept is 3.
X
UA. In solving for the x-intercept, the student's calculation of x is incorrect. The error occurs in
(Type an integer or a decimal.)
OB In solving for the v-intercent the student substituted 0 for x The student should have suhe
Answer:
The error is when 6y = 12 it will be -6y = 12 and the intercept would be -2.
Step-by-step explanation:
simplify the following expression a^2b^-2c^-1 / e^7
Answer:
a²/(b²ce^7)
Step-by-step explanation:
a^2b^-2c^-1 / e^7 =
= a²/(b²ce^7)
