The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.
Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
If we had increased the confidence level, the margin of error also would have increased.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.
The sample size and the estimate are given as follows:
[tex]n = 450, \pi = 0.47[/tex].
The lower and the upper bound of the interval are given, respectively, by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]
The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).
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please help me solve this
Explanation:
The proof can be had by making use of the AAS congruence postulate (twice) and CPCTC.
We start by showing ΔPQY≅ΔPRX, then by showing ΔXQN≅ΔYRN. The proof is then a result of CPCTC.
Proof1. PQ≅PR, ∠Q≅∠R . . . . given
2. ∠P≅∠P . . . . reflexive property of congruence
3. ΔPQY≅ΔPRX . . . . AAS congruence postulate
4. PX≅PY . . . . CPCTC
5. PX+XQ=PQ, PY+YR=PR . . . . segment sum theorem
6. PX+XQ = PY +YR . . . . substitution property
7. PX +XQ = PX +YR . . . . substitution property
8. XQ = YR . . . . subtraction property of equality
9. ∠XNQ≅∠YNR . . . . vertical angles are congruent
10. ΔXNQ≅ΔYNR . . . . AAS congruence postulate
11. XN ≅ YN . . . . CPCTC
__
Additional comment
You probably did steps 1-3 in part (a) of the problem.
The plane is tiled by congruent squares of side length $a$ and congruent pentagons of side lengths $a$ and $\frac{a\sqrt{2}}{2}$, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.
How to determine the percentage?Since the side of the small square is a, then the area of the tile is
given by:
Area of tiles = 9a²
Note: With an area of 9a², 4a² is covered by squares while 5a² by pentagons.
This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:
Percent = 5/9 × 100
Percent = 0.555 × 100
Percent = 55.5 ≈ 56%.
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Complete Question:
The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats .
What is the probability that a kid who goes to the doctor has a sore throat given that he has a fever?
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%
How to determine the probability?The given parameters are:
P(Fever) = 70%
P(Fever and sore throat) = 21%
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:
P = P(Fever and sore throat)/P(Fever)
So, we have:
P = 21%/70%
Evaluate
P = 30%
Hence, the probability is 30%
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Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?
Joel spent 72.5% of his time exercising after playing soccer on Tuesda
How to determine the percentage?The given parameters are
Minutes spent on Tuesday = 27 more minutes than Monday
Total minutes spend = 60
This means that
Tuesday = Monday + 27
Monday + Tuesday = 60
Make Monday the subject in Tuesday = Monday + 27
Monday = Tuesday - 27
Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60
Tuesday - 27 + Tuesday = 60
Evaluate
2 * Tuesday = 87
Divide by 2
Tuesday = 43.5
The percentage of time spent exercising on Tuesday is then calculated as
Percentage = 43.5/60 * 100%
Evaluate the expression
Percentage = 72.5%
Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday
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Write two expressions that have a solution of x = 4.
ASAP!! Ty
Answer:
X multiplied by 2 is 8
X divided by 2 is 4
Step-by-step explanation:
This is the quickest thing i can give you
A rectangle has a length of (3x - 1) and a width of (x + 1). part a determine the perimeter and area of the rectangle as polynomials. part b determine the perimeter and area of the rectangle if x equals 5. part c determine the perimeter and area of the rectangle if x equals 8.
Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
Lets try to solve out the problem,
Length = 3x-1
Width = x+1
Perimeter = 2(l+b)
Area = l*b
Perimeter= 2 (3x-1 + x+1)
P= 8x
Area = (3x-1) (x+1)
=> 3x(x+1) -1 (x+1)
=> 3x^2 + 3x -x -1
=> 3x^2 + 2x -1.
Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..
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Why cant the a value in the standard form of a quadratic function ax^2+bx+c=0 be equal to 0?
Answer:
the equation is no longer quadratic
Step-by-step explanation:
A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.
What happens when a = 0?The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:
bx +c = 0
What term describes the brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats
Refractory period brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats.
At what time is the volume of blood in the ventricle at a maximum?End-diastolic pressure is at its resting level (end-diastolic pressure) and ventricular volumes are at their maximum value when the heart muscle is relaxed (end-diastolic volume).
What is the state of the heart during systole?
Describe what occurs during systole in the heart. Describe where the blood is sent from each ventricle. Right ventricle transfers blood into the pulmonary artery during ventricular contraction and pumps it to the heart.What are the 4 phases of cardiac cycle?
There are four main stages of activity in the cardiac cycle: Isovolumic contraction, inflow, ejection, and relaxation are the order of events. (See Wiggers graphic, which labels the stages in the following order: 3, 4, 1, and 2, from left to right.)Learn more about Refractory period
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A committee of three people needs to be chosen. There are three men and five women available to serve on the committee. If the committee members are randomly chosen, what is the probability that two of the three people chosen on the committee are women
Answer:
probability of choosing two women over people in a community=⅔
On four consecutive statistics quizzes, you receive the scores: 86 96 100 98 what is your median quiz score?
Answer:
98
Step-by-step explanation:
96+100=196
196÷2=98
Answer:
97.
Step-by-step explanation:
86 96 100 98
Place them in order:
86 96 98 100
The median is the middle value of an ascending sequence of numbers.
As there is an even number of values the median is the mean of the 2 middle ones:
So here it is (96 + 98) / 2
= 97.
Alishia rides her bike 45.3 km in 143 minutes. what is her average speed in kilometers per hour?
Average speed of Alishia is 19 kilometers per hour
Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip
Given :
Distance = 45.3 km
Time taken = 143 minutes = 143/60 =2.384 hours
∴ Average speed = 45.3/2.384 = 19 kilometers per hour
Thus the average speed of Alishia is 19 kilometers per hour.
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Outside a home, there is a 4-key keypad numbered 1 through 4. The correct six-digit code will open the garage door. The numbers can be repeated in the code
(a) How many codes are possible?
(b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
(a) The number of possible codes is
(Type an integer or fraction. Simplify your answer)
(b) The probability that the correct code is given on the first try, assuming that the owner doesn't remember it is
(Type an integer or fraction Simplify your answer.)
Using the Fundamental Counting Theorem, it is found that:
a) 256 codes are possible.
b) The probability is [tex]\frac{1}{256}[/tex].
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are 4 keys, each with 4 options, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].
Then the number of codes is:
[tex]N = 4^4 = 256[/tex]
And the probability is:
[tex]p = \frac{1}{256}[/tex].
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A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
The value of the constant of variation include 8, 3.2, and 1.25
How to find the constant?From the information given, when x = -0.5, y = -4.0. The constant will be:
y = kx
-4 = -0.5k
k = -4.0/-0.5
k. = 8
When x = 2.5, y = 8
y = kx
8 = 2.5k
k = 8/2.5
k = 3.2
When x = 4, y = 5
y = kx
5 = 4k
k = 5/4
k = 1.25
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Mark this and retum
S
R
Which statements are true about triangle QRS? Select
three options.
The side opposite ZQ is RS.
The side opposite ZR is RQ.
The hypotenuse is QR.
The side adjacent to ZR is SQ.
The side adjacent to 4Q is QS.
Save and Exit
Next
Submit
The statements that are correct about right triangle QRS are:
Side opposite ∠Q is RS not RQHypotenuse of the right triangle is QRAdjacent side to ∠Q is QSWhat is a Right Triangle?A right triangle posses a right angle which is in opposite direction to the hypotenuse.
Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ, and Adjacent side to ∠Q is QS.
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What is the range of the function f(x) = |x – 3| + 4?
R: {f(x) ∈ ℝ | f(x) ≥ 4}
R: {f(x) ∈ ℝ | f(x) ≤ 4}
R: {f(x) ∈ ℝ | f(x) > 7}
R: {f(x) ∈ ℝ | f(x) < 7}
Answer: R: {f(x) ∈ ℝ | f(x) ≥ 4}
Step-by-step explanation:
[tex]|x-3| \geq 0[/tex] for all real x, so the range is [tex]f(x) \geq 4[/tex].
The side lengths of ABC are 2, 5, and 6, and DEF has side lengths of 12, 30, and 36. Find the ratios of the lengths of the corresponding sides of ABC
to DEF. Are the two triangles similar? Explain. Determine which two of the three given triangles are similar. Find the
scale factor for the pair.
Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.
What are Similar Triangles?The ratios of the corresponding sides of similar triangles are equal, because they are proportional.
If triangles ABC and DEF are similar triangles, then:
AB/DE = BC/EF = AC/DF
Plug in the given values
2/12 = 5/30 = 6/36 = 1/6
This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.
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a) The cosine rule can be used to find the value of x in the triangle below.
What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)
b) What is the value of x? Give your answer to the nearest integer.
Answer:
see explanation
Step-by-step explanation:
(a)
(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )
x² = 12² + 15² - (2 × 12 × 15 × cos71°)
(b)
x² = 144 + 225 - 360cos71°
= 369 - 360cos71° ( take square root of both sides )
x = [tex]\sqrt{369-360cos71}[/tex]
≈ 16 cm ( to the nearest integer )
The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is symbolized by _____.
Considering that the value of 126.07 is valid for the population, it is a parameter.
What is the difference between a statistic and a parameter?If the measure is defined only for the sample, it is a statistic.If the measure can be defined for the population, it is a parameter.In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.
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Adam runs 100m in 14.5 seconds. Jenny runs the same distance 10% faster. How long does it take for Jenny to finish?
The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds
PercentageDistance Adam runs = 100mTime taken by Adam = 14.5 secondsDistance Jenny runs = 100mTime taken by Jenny = 14.5 - (10% × 14.5)
= 14.5 - (0.1 × 14.5)
= 14.5 - (1.45)
= 13.05 seconds
Therefore, the time taken for Jenny to run the same distance is 13.05 seconds
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A random sample of n = 16 scores is obtained from a normal population with m = 40 and s = 8. what is the probability that the sample mean will be within 2 points of the population mean?
Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]
The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:
X = 42:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (42 - 40)/2
Z = 1
Z = 1 has a p-value of 0.8413.
X = 38:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (38 - 40)/2
Z = -1
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
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A bakery offers a sale price of $3.30 for 3 muffins. what is the price per dozen?
Answer:
$13.20
Step-by-step explanation:
A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.
3.30*4=13.20
The standard deviation tells us a. the average value of the scores. b. the relative standing of a particular score. c. the skewness of the distribution. d. the dispersion of the scores.
Answer:
D.
Step-by-step explanation:
Standard deviation tells us the dispersion of data/scores around the mean.
We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
What is the standard deviation?A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.
We use the following formula to compute the standard deviation:
[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]
In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.
How to solve the question?In the question, we are asked to tell what standard deviations tell us from the given options.
From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.
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Solve each equation
Note:now you need to perform inverse operations to solve for the variables. For example in (2/3x -6) try adding 6 to both sides first then multiply the reciprocal of 2/3 (meaning the flipped version)
The factorise form of the two expression are as follows:
2 (x - 3) (x - 9)-3(x + 5)(x + 7) How to solve an expression?b. (x - 3)(2 / 3 x - 6) = 0
Therefore, let's open the brackets
2 / 3 x² - 6x -2x + 18 = 0
2 / 3 x² - 8x + 18 = 0
multiply through by 3
2x² - 24x + 54 = 0
Hence,
2 (x - 3) (x - 9)
c.
(-3x - 15)(x + 7) = 0
Therefore,
-3x² - 21x - 15x - 105 = 0
-3x² - 36x - 105 = 0
-3(x + 5)(x + 7)
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Which relationship describes a function?
O (bedrooms, sale price)
(acres of land, appraised value)
(sale price, bedrooms)
(appraised value, property tax)
The relationship which best defines a function, for the houses on Katrina's street exists appraised value, property tax.
How to read the data from the table?Table exists a form to describe the data of the two or more variables.
To read the data from the table, examine for the value of one variable, and obtain the resultant value of other variables from the related block.
The table below details some of the characteristics of the houses on Katrina’s street. Let's estimate the most suitable choice whose relationship defines a function.
The function exists in the relationship between various variables. This relation or the expression provides the output, by accepting some input value of variables.The output for a function is related to the input and provides various outputs with various input values.Only appraised value and property tax, in the given table, supplies a unique value per time.The relationship which nicely illustrates the function, of the houses on Katrina's street exists between the appraised value and property tax.
Therefore, the correct answer is option d) (appraised value, property tax).
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Answer: D
Step-by-step explanation: Appraised Value , Property Tax
What is the solution to the equation − = − − ? show your work.
The solution to the equation is 2
How to determine the solutionGiven the equation
4 + 4(x-2) = 2(x+1) - x
First, we expand the bracket
4 + 4x - 8 = 2x + 2 - x
collect like terms
4x - 2x + x = 2 - 4 + 8
Add like terms
3x = 6
Make 'x' the subject
x = 6/3
x = 2
Thus, the solution to the equation is 2
The complete question is
What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work
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(6x - 4)(3 - 2x)/4x - 6
[tex] \frac{(6x - 4)(3 - 2x)}{(4x - 6)} = \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} [/tex]
[tex] \frac{2(3x - 2)(3 - 2x)}{2(2x - 3)} = \frac{(3x - 2)(3 - 2x)}{(2x - 3)} [/tex]
[tex] \frac{(3x - 2)(3 - 2x)}{(2x - 3)} = \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} [/tex]
[tex] \frac{ - (3x - 2)(2x - 3)}{(2x - 3)} = - (3x - 2)[/tex]
[tex] - (3x - 2) = 2 - 3x[/tex]
A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured in square millimeters (mm2). The sample mean is 346.5 mm2 and sample standard deviation is 170.38 mm2. The 95 percent confidence interval for the mean is:
The 95 percent confidence interval for the mean is (266.76,426.24).
A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.
The formula of Confidence Interval = Mean ± [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]
where t is a constant
Given:
Mean = 346.5
Standard Deviation = 170.378
t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093
∴ Substituting values in formula we get
E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74
95% Confidence interval : (346.5-79.74,346.5+79.74)
95% Confidence interval : (266.76,426.24)
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pls help me on this one :((
Answer:
B
Step-by-step explanation:
Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.
This is equal to c(d+b), so:
(1/2)(c)(2d+a+b)=c(d+b)
(1/2)(2d+a+b)=d+b
d+0.5a+0.5b=d+b
0.5a+0.5b=b
0.5a=0.5b
a=b
Solve the equation. Simplify your answer.
2 (3-x) = 16 (x+1)