Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean and standard deviation , as long as[tex]np\geq 10[/tex] and [tex]n(1-p)\geq 10[/tex]From the equation of the standard error, we could see that if one of the conditions is not respected, the standard error would be very high, indicating a low accuracy of the estimate, hence it is found that these conditions are required to avoid the high variability associated with small samples.[tex]s=\sqrt{p(1-p)/n}[/tex]
If we compare the p value and using the significance level given [tex]\alpha=0.05[/tex] we have[tex]pv > \alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.[tex]p v=2*p(z < -0.531)=0.595[/tex]
1) Data given and notation
n=500 represent the random sample taken
X=380 represent the number of people with some characteristic
estimated proportion of adults that said that it is morally wrong to not report all income on tax returns
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1) The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.
b) The sample needs to be large enough
3) Calculate the statistic
[tex]z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}[/tex]
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha =0.05[/tex]The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]pv=2*p(z < -0.0531)=0.595[/tex]
If we compare the p value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.
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Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f() = 6sec + 3tan , 0 < < 2
The critical numbers of the function are; θ = π/6, 5π/6
How to find the critical value of a trigonometric function?
We are given the trigonometric function as;
f(θ) = 6secθ + 3tanθ ; 0 < θ < 2π
The critical points of a function are defined as those points of the domain where the function is not differentiable or those points for which the derivative is equal to zero.
Let us find the first derivative;
f'(θ) = 6(-sin θ/cos² θ) + 3(1/cos² θ)
f'(θ) = (3 - 6sin θ)/cos² θ
At f'(θ) = 0, we have;
3 - 6sin θ = 0
θ = sin⁻¹(3/6)
Since sin is positive, then;
θ = π/6, 5π/6
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Elvia has a bag of snack mix that contains 5 cereal pieces, 4 peanuts, 5 pretzels, and 1 bagel chip. Suppose that she is equally likely to pick any individual object from the bag. What is the probability that Elvia will randomly pull a pretzel from the bag?
Answer: 33%
Step-by-step explanation: a third of the items in the bag are pretzels.
what IS 1/2 as a percent help pls SOS
Answer:
50%
Step-by-step explanation:
numerator divided by denominator
1 divided by 2 = .5
.5 x 100 = 50%
An isosceles triangle has an angle that measures 140°. What measures are possible for
the other two angles? Choose all that apply.
Recommendations
15⁰
70°
45°
20•
The possible value of other two angles will be 20 degree.
What are the types of triangle?
Basically, there are six different types of triangles in terms of lengths and measurements of triangle lines or angles. The sum of all interior angles of a triangle is always 180 degrees. This is called the angular summation of the triangle. Depending on the length of the sides, triangles can be divided into three types:
scale
Isosceles
equilateral
It is given that an isosceles triangle has an angle that measures 140°
We know that two sides of isosceles triangle are equal and by the property of triangle we know that angle opposite to equal sides are equal therefore remaning two angles of isosceles triangle will be equal.
Let the angles be x
By angle sum property of triangle
x + x + 140 = 180
2x = 180 - 140
2x = 40
x = 40/2 = 20
Therefore, the possible value of other two angles will be 20 degree.
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Let F be any nonconstant vector field of the form F = f (x) i + g (y) j + h (z) k and let G be any nonconservative vector field of the form G = f (y, z) i + g (x, z)j + h (x, y) k. Indicate whether the following statements are true or false by placing ''T'' or ''F'' to the left of the statement. 1. G is incompressible 2. F is irrotational 3. G is irrotational 4. F is incompressible
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .
So if we calculate for F:
F has a divergence potentially
divF = df/dx + dg/fy + dh/dz
But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)
For G
G has zero divergence.
divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0
But it may have a curl.
curl(G) = df/dy may be non-zero
df/dz, dg/dx etc may all be non-zero
Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,
div = 0 = incompressible and
curl = 0= irrotational
Thus,
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
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Help me please
dont even need a full explanation just answer
The correct option C: -4 ≤ x ≤ -2, are the intervals in which the graph is constant.
Explain the term constant function?An algebraic expression known as a linear expression has terms that are either constants or variables raised to first power. Alternatively put, no of the exponents could be greater than 1.A linear function with a slope of 0 is known as a constant function. The function's value will remain constant regardless of the value you select for "x." A constant function has a graph that is a horizontal line and through y-intercept, "b." Example A's graph is indeed a horizontal line that passes through y = 4 since b is equal to 4.So, from the shown graph, the horizontal line have the constant function which lies in the intervals -4 ≤ x ≤ -2.
Thus, in the intervals -4 ≤ x ≤ -2, the function is constant.
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It takes a bus 1 hour and 30 minutes to travel 42 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
28 mph is the average speed of the bus in mph.
What is speed?
The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.
Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.
time = (1+ 1/2)hr = 3/2 hr = 1.5 hr
distance = 42 miles
average speed = total distance/total time
42/1.5 = 28 mph
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select the spreadsheet formula that would correctly calculate the average (mean) of the following values: 25, 50, and 75.
The spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.
What is an average?An average is a single number taken as representative of a list of numbers, generally the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).
What is the formula to calculate the average?The formula to calculate the average of given numbers is equal to the sum of all the values divided by the total number of values. Average = Sum of Values / Number of Values.
So, in this case:
Values: 25, 50, 75
Number of Values: 3
Thus, the average:
Sum of Values / Number of Values = (25 + 50 + 75) / 3 = 50
Hence, the spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.
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Which statement about Shawn’s line is true?
The slope of the line is 1/3
The y-intersect of the line is (4,0)
The y-interpect means Shawn ran 4 laps at week 0
The slope represents the average number of weeks it is Shawn to run laps
The slope represents the average number of weeks it is Shawn to run laps is true about Shawn's line.
Define slope.The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
Given,
Graph to show number of taps he is scheduled to run a week.
True statement is,
The slope represents the average number of weeks it is Shawn to run laps.
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Enter numbers to evaluate ‐6−13. ‐6−13= ‐6 + = Enter numbers to evaluate ‐6−(‐13). ‐6−(‐13)= ‐6 + =
The given expression evaluates to -19.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following expression -
- 6 - 13
The given expression evaluates to -
x = - 6 - 13
x = - 19
Therefore, the given expression evaluates to -19.
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Find the sum of 3x + 2 and 8x
4-1 3/5 write as a mix number in simplest form
Answer:
Step-by-step explanation:
17/5
Answer:
2 and 2/5
Step-by-step explanation:
A water tank initially contained 57 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many minutes have passed m when the tank contains 35 liters? Round go the nearest tenth
Answer:
8.8 minutes
Step-by-step explanation:
first we figure out how many liters are being lost
57 - 35 = 22
then divide that by 2.5
22 / 2.5 = 8.8
8.8 minutes
if f(a)=a²-1 find f(5)
Answer: 24
Step-by-step explanation:
A=5 so F(x)=5^2-1
F(x)=24
Solve the problems.
Write the complete proof in your paper homework and for online to questions or statements (if any) that are parts of your proof
Given m ∠A=m ∠C=90°
AB ║ DC
Prove Δ ABD ≅ Δ CDB
Answer= m ∠ABD= m ∠CDB by reason ____
By AAS congruence theorem, ΔABD is congruent ΔCDB.
Quadrilateral ABCD is given in the figure.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given, AB║DC
Consider ΔABD and ΔCDB
m∠A=m∠C=90° (Given)
m∠ABD=m∠BDC (Alternate interior angles)
BD = BD (Common)
Using AAS congruence theorem, ΔABD ≅ ΔCDB
Hence, by AAS congruence theorem, ΔABD is congruent ΔCDB.
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ING
DO
S
DO
Here's the revenue and expenses for the month. Calculate whether Mia had a profit or loss.
REVENUE
DOG FOOD
$3,500
CAT FOOD
$2,100
PET TREATS
$1,200
PET SUPPLIES $2,750
TOTAL
$9,550
JANUARY ACCOUNTS
FIXED EXPENSES
RENT
$2,000
SALARIES
$2,000
UTILITIES
$1,000
PRODUCT STOCK $4,000
TOTAL
$9,000
$ X
VARIABLE EXPENSES
NEWSPAPER AD $200
TOTAL
$200
ENTER MIA'S TOTAL PROFIT/LOSS FOR THE MONTH IN THE BOX BELOW, THEN CLICK SUBMIT.
SUBMIT
Create a slope intercept equation with given information (3,1) m =0
Answer:
y = x - 2
Step-by-step explanation:
Since m = 0, what we have so far is y=x+b
We have a point, which is (3,1)
Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).
1=3+b
1-3=3+b-3 undo the 3 by subtracting
-2 = b
y = x + -2 simplify
y = x - 2
Which inequality has the graph shown below?
The inequality is y > 2x-3
option C is correct
What is inequality in math?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
The line intersects the y- axis at point (0,-3)
i.e., The y-intercept =-3
We know that,
Equation of lime, y= mx + b
b: y-intercept
m: Slope of the line
Slope of the line,
m = 0-(-3)/3/2 = 2
m ⇒ 2
∴ Equation of line, y = 2x - 3
The shaded are is above the line, and line is represented with dotted lines,
hence the inequality is,
y > 2x - 3
Hence, option C is correct
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when an article is sold for 1200 there is 10% profit at what price should it be sold to gain 20%
Answer:
1309.10
Step-by-step explanation:
1200 = 110%
(1200/110)*120 = 1309.10
an object travels 4/5 miles in 1/2 hour. what is her speed?
Answer:
[tex]\huge\boxed{\sf v = 0.4\ mph}[/tex]
Step-by-step explanation:
Given data:Distance = S = 4/5 miles = 0.2 miles
Time = t = 1/2 hour = 0.5 hours
Required:Speed = v = ?
Formula:v = S/t
Solution:v = 0.2/0.5
v = 0.4 mph[tex]\rule[225]{225}{2}[/tex]
Answer: 8/5 mph
Step-by-step explanation:
According to definition, an object's speed is determined by:
s=d/t where,
d is the object's travel distance, and t is the amount of time it takes.
We can replace these values with:
Since, s= (4/5) / (1/2) mph
=> s= 8/5 mph
The object's speed to cover 4/5 miles in 30 minutes is: 8/5 mph
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex: (2, 3); point: (0, 2)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]
The size of a population is modeled by the function P that satisfies the logistic differential equation dP/dt=(1/10)P - (1/5000)P^2 , where t is measured in months and P (0) = 50. What is the size of the population at the moment when the population is growing most rapidly? A. 50 B. 250 C.500 D. 2500
The correct answer is A.
500 is the size of the population at the moment of maximum growth.
Given data:
To find the size of the population at the moment when the population is growing most rapidly, we need to determine the maximum value of the derivative dP/dt.
Given the logistic differential equation [tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex], find the derivative by taking the derivative of each term separately:
[tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex]
To find the critical points where the derivative is zero or undefined, set dP/dt equal to zero:
[tex](\frac{1}{10})P - (\frac{1}{5000})P^2=0[/tex]
Simplifying:
[tex](\frac{1}{10})P= (\frac{1}{5000})P^2[/tex]
[tex]10P^2=5000P[/tex]
Dividing both sides by P and rearranging:
[tex]10P(P-500)=0[/tex]
This equation has two solutions: P = 0 and P = 500.
To determine which solution corresponds to the moment when the population is growing most rapidly, examine the second derivative. Taking the second derivative of the logistic differential equation, we have:
[tex]\frac{d^2P}{dt^2} = \frac{1}{10} - \frac{2}{5000}P[/tex]
Evaluating the second derivative at P = 0 and P = 500, we get:
[tex]\frac{d^2P}{dt^2}_{P=0} = \frac{1}{10} - \frac{2}{5000}(0)[/tex]
[tex]\frac{d^2P}{dt^2}_{P=0}= \frac{1}{10} > 0[/tex]
[tex]\frac{d^2P}{dt^2}_{P=500} = \frac{1}{10} - \frac{2}{5000}(500)[/tex]
[tex]\frac{d^2P}{dt^2}_{P=0}= -\frac{1}{10} < 0[/tex]
Since the second derivative is positive at P = 0 and negative at P = 500, the moment when the population is growing most rapidly occurs at P = 500.
Hence, the size of the population at the moment when the population is growing most rapidly is 500.
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4x - 8y = -4
-2x + 8y = -2
Solve by elimination
Answer:
X=1 Y=0
Step-by-step explanation:
Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x
4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0
Now, knowing that y=0, plug y into the second equation:
-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1
PLEASE HELP AGAIN I STILL NEED TO GET THESE DONE
Answer:
........................
A store bought a sofa wholesale for 200 and marked it up 15% when the sofa did int sell they reduced the price 15% show why the current price is not 200
Answer:
The current price of sofa is $195.50.
Step by Step explanation:Cost price of the sofa for the store = $200
Now, the store marked it up 15%.
So, marked price of sofa = $200 + 15% of $200
=200 + 30
=$230
Now, it is given that the sofa could not sell at this price. So, the store reduces its price by 15% now.
So, current price of sofa = $230 - 15% of $230
= 230 - 34.5
=$195.5
So, the current price of the sofa is $195.50.
2. If AJKL AQRS, find each missing value.
R
J
3x-1
58°
32
(4z + 3)°
K
L
27
Q
y + 10
87⁰
14
S
X=
Y=
Z=
4
Answer:gat big
Step-by-step explanation:
Dr. Arman has 1,000
vitamin samples to give his
patients. The number of
samples remaining
decreases by 18% each
week. Which equation
represents the remaining
number of samples after x
weeks?
1000 - 180x represents the remaining number of samples after x weeks.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Main body:
Consider what is actually happening in the question.
You begin with 1000 samples, after it decreases to
=1000-18% of 1000
= 820
You can see the pattern shows that the number of samples decreases 18% every week ,1000-18% of 1000 - 18% 0f 1000.
= 1000 - 180x where x denotes number of weeks.
Hence 1000 - 180x represents the remaining number of samples after x weeks.
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Simplify. Show your work. Circle your answer.
2√10·5√12
Simplify the [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] we will get 20 · √30.
What do you mean by exponent and radicals?
Exponents are a convenient way of describing repeated multiplication of the same number. Radicals include the use of radical characters √
These are sometimes called surdos. The exponent is the power p of an expression of the form [tex]a^{p}[/tex]
The process of raising a base number to a given power is called exponentiation. (where a ≠ 0)
Given:
[tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex]
= (2 × 5)· [tex](\sqrt{10}\times \sqrt{12)}[/tex]
= 10 · [tex]\sqrt{120}[/tex]
= 10 · 2 · [tex]\sqrt{30}[/tex]
= 20 · √30
Therefore, [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] = 20 · √30
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1/2 of the animals at the shelter are cats. If there are 318
animals at the shelter, how many are cats?
Answer:
159
Step-by-step explanation:
To find half of an amount, multiply the amount by 1/2 which is the same as dividing the amount by 2.
318 × 1/2 =
= 318 ÷ 2
159
-----------------------
2 | 318
- 2
------------
11
- 10
-------
18
- 18
------
0
318 × 1/2 = 318 ÷ 2 = 159
“According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answer to three decimal places, for example: 0.123]”
A probability is a numerical representation of the likelihood or chance that a specific event will take place.
How to find the probabilities?12% of peanut M&M’s = brown
15% = yellow
12% = red
23% = blue
23% = orange
15% = green
Here, Probability of an event is represented as P
a) P(not green) = 100% - 15%
= 85%
= 0.85
b) P(yellow or red) = 15% + 12%
= 27%
= 0.27
c) P(three blue) = 0.23*0.23 *0.23
= 0.012 (rounded to 3 decimal places)
d) P(not green if you choose 6 )= [tex](0.85)^{6}[/tex]
= 0. 377
e) P(at least 1 green if you choose 6 ) = 1 - 0.377
= 0.623
What is probability?Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, probability has been introduced in mathematics. The degree to which something is likely to happen is essentially the definition of probability. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. We must first determine the total number of outcomes in order to calculate the probability that a single event will occur.To learn more about probability, refer:
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