In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6967 subjects randomly selected from an online group involved with ears. There were 1331 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution.
Answers
Answer:
\(z=\frac{0.191 -0.2}{\sqrt{\frac{0.2(1-0.2)}{6967}}}=-1.878\)
Now we can find the p value using the alternative hypothesis and with the following probability:
\(p_v =P(z<-1.878)=0.0302\)
We see that the p value is higher than the significance level of 0.01 so then we FAIL to reject the null hypothesis and there is NOT enough evidence to conclude that the return rate is less than 20% at 1% of significance
Step-by-step explanation:
Information given
n=6967 represent the random sample selected
X=1331 represent the surveys returned
\(\hat p=\frac{1331}{6967}=0.192\) estimated proportion of return rate
tex]p_o=0.2\) is the value to verify
\(\alpha=0.01\) represent the significance level
z would represent the statistic
\(p_v\) represent the p value
System of hypothesis
We test the claim that the return rate is less than 20%, then the system of hypothesis are:
Null hypothesis:\(p\geq 0.2\)
Alternative hypothesis:\(p < 0.2\)
The statistic is given by:
\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)
Replacing the info given we got:
\(z=\frac{0.191 -0.2}{\sqrt{\frac{0.2(1-0.2)}{6967}}}=-1.878\)
Now we can find the p value using the alternative hypothesis and with the following probability:
\(p_v =P(z<-1.878)=0.0302\)
We see that the p value is higher than the significance level of 0.01 so then we FAIL to reject the null hypothesis and there is NOT enough evidence to conclude that the return rate is less than 20% at 1% of significance
Related Questions
A high-end interior designer charges an hourly rate for his services plus a consultation fee. As a courtesy to his clients, after working on a job for over 20 hours, his hourly rate drops and the consultation fee is waived. The fees for the interior designer's services can be modeled with the following piecewise equation, where x represents the number of hours. f(x)={150x+300, x≤20100x, x>20 How much would it cost for 18 hours of interior design services? Enter your answer in the box. $
Answers
Answer:
3000
Step-by-step explanation:
Find the surface area of the box shown
Answers
3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)
Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.
Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.
Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.
Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.
Answers
Answer:
The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.
Step-by-step explanation:
raise t to the 10th power then add the result to 3
Answers
The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3
How to write algebraic expressions?
An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.
Given: raise t to the 10th power then add the result to 3
Note: t is the variable here
Let's write algebraic expression now:
raise t to the 10th power => t¹⁰
then add the result to 3 => t¹⁰ + 3
Therefore, the algebraic expression is t¹⁰ + 3
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Becca decided to drink 4 liters of water every day. There are approximately 29.6 milliliters in 1 fluid Ounce. Which measurement
is closest to the number of fluid ounces in 4 liters?
Answers
Answer:
i think 6
Step-by-step explanation:
i looked it up
Answer:
135
Step-by-step explanation:
took test
HELP ME THSI IS DuE TOMOROW
Answers
y = mx + b is what the equation will be our equation...
m = 9/10
b=-495
(Since s is the variable for salary, the new equation is y=ms+b.)
y = 0.9s - 495
495 = 0.9s (Divide by 0.9)
s = 550
(I hope I'm right)
A rectangular prism has dimensions of 2 cm by 2 cm by 5 cm. What is the surface area? Explain or show your reasoning?
Answers
Answer:ehhwvwhsv
Step-by-step explanation:
i.e ;
l = 2cm
b = 2cm
h = 5cm
SA of rectangular prism = 2(lb + bh + hl)
Put values.
SA = 2(2×2 + 2×5 + 5×2)
= 2× 24
Suppose you model a game of chance with a discrete probability distribution. Let X be the net amount of money won or lost by the player. Let P ( X ) be the probability of the corresponding outcome. The three events are as follows: There is a 23% chance the player wins 5 dollars. There is a 29% chance the player breaks even. There is a 48% chance the player loses 3 dollars. Complete the table below to model the scenario
Answers
Mathematicians have used probability to determine how likely certain events are to occur. The possible values of X will be 10, 0, -5 with following probabilities:
P(X = 10 ) = 0.23
P(X = 0 ) = 0.48
P(X = -5) = 0.29
What in mathematics is probability?Probability is the ability to happen. . From 0 to 1 is used to express the value. Whenever we are unsure of how an event will turn out, we can talk about the probabilities of various outcomes, or how likely they are. The study of probability-based events is often known as statistics. The amount of favorable outcomes and the overall number of outcomes thus affect how likely an event is to occur. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space.
Given:
The probability distribution of X can be represented as:
X P(X=x)
-5 0.29
0 0.48
10 0.23
The outcomes is attached as table below.
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The complete question is:
The table below to model the scenario is attached below:
area if room 14.5m long
and 20.3 wide is
Answers
List all possible rational zeroes for the function. Enter your answer as a comma separated list.
Answers
Answer:
no zeros
Explanation:
The zeros of our function will be the x values that are solutions to
\(f(x)=x^4+3x^3-4x+4=0\)Meaning, the points at which the function intersects the x- axis ( because that is where y = f(x) = 0)
Plotting the function gives
We see that the function does not intersect the x-axis at any point. Therefore, the function does not have any zeros.
Tim purchases 3,000 shares in company X at $2.49 per share. The company subsequently announces a profit warning, and the share price drops to $2.24 per share. Wishing to minimise his losses, Tim decides to sell his shares. How much of a loss does Tim make? Give your answer in dollars to the nearest dollar
Answers
Answer:
$750
Step-by-step explanation:
Tim's share price changes by $2.24 -2.49 = -0.25, so the change in the value of his investment is ...
(3000 shares)(-0.25/share) = -$750
Tim takes a loss of $750 when he sells.
Answer:
Step-by-step explanation:
$\$1170$
Bob's initial investment is given by
Initial Investment =3,000×$1.25=$3,750.
When Bob sells the shares, he sells them for
Sold for price=3,000×$0.86=$2,580.
Therefore Bob's total LOSS is given by
Loss =$3,750−$2,580=$1,170.
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is accurate, what is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Answers
Answer:
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
This means that \(p = 0.07\)
Sample of 459 phone calls:
This means that \(n = 459\)
Mean and standard deviation:
\(\mu = p = 0.07\)
\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119\)
What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?
Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.
Probability the proportion is below 0.04.
p-value of Z when X = 0.04. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{0.04 - 0.07}{0.0119}\)
\(Z = -2.52\)
\(Z = -2.52\) has a p-value of 0.0059
2*0.0059 = 0.0118
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
The state of Alaska saw a population increase of 3.3% since 2010. What is the growth factor over this time?
Thank you
Answers
Answer:
To find the growth factor, we need to first convert the percentage increase to a decimal:
3.3% = 0.033
The growth factor is then calculated as:
1 + percentage increase as a decimal = 1 + 0.033 = 1.033
Therefore, the growth factor over this time is 1.033. This means that the population of Alaska increased by a factor of 1.033 since 2010.
What are the solutions to the equation (x2-21)2=25?
Answers
The solutions to the equation (x² - 21)² = 25 are x = 4, x = -4, x = √26, and x = -√26.
How to determine the vertex form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this equation, we can determine the solutions as follows:
(x² - 21)² = 25
By taking the square root of both sides of the equation, we have the following:
√(x² - 21)² = √25
x² - 21 = 5
x² = ±5 + 21
x = ±√26
x = ±√16 = 4
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Complete Question:
What are the solutions to the equation (x² - 21)² = 25?
Need help with this question. PLS helpppppp
Answers
Answer:
x = 0.39 or
x = -1.72
Step-by-step explanation:
The quadrateic formula is:
\(x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}\)
eq: 3x² + 4x - 2
which is of the form ax² + bx + c = 0
where a = 3, b = 4 and c = -2
sub in quadratic formuls,
\(x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72\)
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
15 POINTS HELP!!!
Al and Tim each have rectangular wooden decks on their homes. Al’s deck is 4 feet wide and has an area of 60 x+40 ft². Tim’s deck is 7 feet wide and has an area of 21x+14 ft². Determine an expression for the length of each deck. How many times the length of Tim's deck is Al’s deck?
Answers
The length of Tim's deck is 1/15th of the length of Al's deck.
Finding the expressions for the length of each deck.
For Al's deck:
Area of a rectangle = length × width
60x + 40 = length × 4
length = (60x + 40) / 4
length = 15x + 10 ft
For Tim's deck:
Area of a rectangle = length × width
21x + 14 = length × 7
length = (21x + 14) / 7
length = 3x + 2 ft
Now we can find no. of times the length of Tim's deck is Al's deck by dividing the length of Al's deck by the length of Tim's deck:
(15x + 10) / (3x + 2)
Simplifying this expression:
(3(5x + 3) + 1) / (3x + 2)
(3(5x + 3) / (3x + 2)) + (1 / (3x + 2))
15 + (1 / (3x + 2))
Therefore, the length of Tim's deck is 1/15th of the length of Al's deck.
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Can someone help please?
Answers
Answer:
2
mark me as brainliest..........
Answer:
2
Step-by-step explanation:
since they are similar
they will be divided by 9 for example
we have 54 on the left but if you divide it by 9 we get 6 which is on the right
then we have 27 on the left if you divide by 9 we get 3 which is on the right
so then we have 18 and a missing number
so we divide 18/9 and get 2
If x = 2, solve for y. y = 6.3x y=[?]
Answers
Answer: y = 12.6
Step-by-step explanation:
Since x = 2 and y = 6.3 * x, y = 6.3 * 2.
6.3 * 2 is equal to 12.6, so y is 12.6.
Answer:
y = 12.6
Step-by-step explanation:
y = 6.3x x = 2
Solve for y.
y = 6.3(2)
y = 12.6
So, the answer is 12.6
Alvin is 7 years younger than Elgas. The sum of their ages is 63. What is Elgas age?
Answers
Answer:
Elgas is 35.
Step-by-step explanation:
Let's set up an equation.
Alvin is 7 years younger than Elgas.
A = E - 7
The sum of their ages is 63.
A + E = 63
Let's use substitution.
Plug in the first equation of A into the second equation.
A + E = 63
(E - 7) + E = 63
Combine like terms.
2E - 7 = 63
Add 7 to both sides.
2E = 70
Divide both sides by 2.
E = 35
Elgas is 35.
Hope this helps!
first person to answer will get brainliest.
Answers
Answer:
the first one because x's don't repeat in this one
Step-by-step explanation:
Find sin 8.
45
53
28
8
Answers
Answer:
A. 45/53
Step-by-step explanation:
.............
Answer:
A. 45/53
Step-by-step explanation:
sin ø is A.
have a nice day
Triangle ABC has the vertices A(2, 0), B(4, 2), and C(3, 4).
Name the ordered pair of C' after a reflection across the
x-axis.
Answers
Answer: C’(3,-4)
Step-by-step explanation: All you have to do is count how many blocks away is the point from the x axis and then count down the x axis where you stop counting and that is how you get your point.
Every time Juan runs, he runs 2/3 of a mile. Whenever Leslie runs, she runs 3/3 of a mile. If Juan runs 6
times a week, how many times must Leslie run to cover the same distance as Juan?
Answers
Answer:
4
Step-by-step explanation:
This is a simple multiplication problem. First, you would multiply 2/3 by 6 to see how miles Juan runs per week. That's 12/3, or 4 miles. Then, you would divide 4 by 3/3 to see how many times Leslie must run. That's 4 times.
Answer:
run 3 is a game where you have to trie to collect all of the characters
Step-by-step explanation:
video game
What is the distance between (2,8) and (7,7)
Answers
Answer:
5.1 units
Step-by-step explanation:
Hey there!
To find the distance of points,
(2,8) and (7,7).
We need to use the Pythagorean Theurom formula which is,
\(a^2 + b^2 = c^2\)
So we need to find the rise/run or a and b to find c or the distance.
x - 2 and 7, distance of 5 units
y - 8 and 7, distance of 1 unit.
Plug those numbers in.
\(5^2 + 1^2 = c^2\)
25 + 1 = c^2
26 = c^2
c = 5.09901
c = 5.1 rounded to the nearest tenth.
Hope this helps :)
Here is how i did it
Given y=4x+2, find the domain value if the range value is 4
Answers
4-2=4x+2-2
2=4x
Divided both sides by 4
X=1\2
The domain value that corresponds to a range value of 4 is,
⇒ x = 1/2
Given that;
Function is,
y = 4x + 2
Since, the equation equal to the range value:
4 = 4x + 2
Then, we can solve for "x":
4 - 2 = 4x
2 = 4x
x = 1/2
Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:
y = 4x + 2
y = 4(1/2) + 2
y = 4 + 2
y = 6
Therefore, the domain value that corresponds to a range value of 4 is,
⇒ x = 1/2
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Arrange the steps in order to simplify the expression
Answers
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
The function f(x) = −23x + 4 represents the average number of teacher absences due to illness, f(x), when the school uses x bottles of hand sanitizer per month. What is a reasonable domain for the function in this situation?
Answers
Given that there exist undefinable restrictions, the domain for the function f(x)=23x + 4 is (-∞,∞).
What is function?In mathematics, a function is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Four main categories may be used to classify different sorts of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Here,
f(x)=−23x+4
as there are undefined constraints,
domain=(-∞,∞)
The domain for function f(x)=−23x + 4 is (-∞,∞) as there are undefined constraints.
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A population declines by 0.7% each year. By what percentage does it decline each decade? (Round your answer to two decimal
places.)
X %
Answers
6.78%
Explanations;If a population declines by 0.7% each year, then the remaining population will be (1-0.7%) of the previous year.
This can be expressed after one decade (10 years) as;
\(\begin{gathered} p=(1-\frac{0.7}{100})^{10} \\ p=(1-0.007)^{10} \\ p=(0.993)^{10} \\ p=0.9322 \end{gathered}\)The percentage of decline per decade will be expressed as:
\(\begin{gathered} \%decline=1-0.9322 \\ \%decline=0.0678=6.78\% \\ \end{gathered}\)This shows that the population declines each decade by 6.78%
A fancy restaurant put dishes of butter at each table. They divided 4/5 of a kilogram of butter evenly to put 1/5 of a kilogram in each dish. How many butter dishes did they fill?
Answers
Answer: 4
This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.
4/5 ÷ 1/5
Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:
4/5 x 5
To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.
You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.
Hope this helps!