Answer:
(a) matched pair design
(b) n = 30
(c) Reject the null hypothesis.
Step-by-step explanation:
The complete question is:
A researcher records the amount of time (in minutes) that parent child pairs spend on social networking sites to test whether they show any generational differences. From the following findings in APA format, interpret these results by stating the research design used (repeated measures or matched pairs), the sample size, the decision, and the effect size. Parents spend significantly less time on social networking sites compared their children (MD = -42 minutes),t(29)=4.021,p<.05,d=0.49.(a) What research design was used? (Repeated measures or matched pairs?)(b) What is the sample size? (n = ?)(c) What is the decision? (Retain or reject the null?)
Solution:
(a)
It s provided that the researcher records the amount of time (in minutes) that parent-child pairs spend on social networking sites.
This implies that the data collected is in the form of paired data.
Thus, the research design that was used was matched pair design.
(b)
Consider the t-statistics provided:
t (29) = 4.021
The number 29 in the bracket is the degrees of freedom.
The degrees of freedom for a matched pair design is,
df = n - 1
Compute the value of n as follows:
df = n - 1
29 = n - 1
n = 29 + 1
n = 30
Thus, the sample size is n = 30.
(c)
The p-value of the test is:
p < 0.05
The p-value of the test is less than the 5% significance level.
This implies that the null hypothesis will be rejected at 5% significance level.
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Perform the operation 3/a^2+2/ab^2
Answer:
Step-by-step explanation:
Least common denominator = a²b²
[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]
The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x¯? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.
Answer:
69.5Step-by-step explanation:
Given the confidence interval of the heights of american heights given as (65.3,73.7);
Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7
Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]
[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]
Hence, the sample mean is 69.5
Suppose you just purchased a digital music player and have put 12 tracks on it. After listening to them you decide that you like 2 of the songs. With the random feature on your player, each of the 12 songs is played once in random order. Find the probability that among the first two songs played (a) You like both of them. Would this be unusual? (b) You like neither of them. (c) You like exactly one of them. (d) Redo (a)-(c) if a song can be replayed before all 12 songs are played.
Answer:
The answer is below
Step-by-step explanation:
We have the following information:
Number of songs you like = 2
Total number of songs = 12
a) P(you like both of them) = 2/12 x 1/11 = 0.015
This is unusual because the probability of the event is less than 0.05
b) P(you like neither of them) = 10/12 x 9/11 = 0.68
c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30
d) If a song can be replayed before all 12,
P(you like both of them) = 2/12 x 2/12 =0.027
This is unusual because the probability of the event is less than 0.05
P(you like neither of them) = 9/12 x 9/12 = 0.5625
P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25
The perimeter of a triangle is 82 feet. One side of the triangle is 2 times the second side. The third side is 2 feet longer than the second side. Find the length of each side.
Answer:
Side 1: 40 feet
Side 2: 20 feet
Side 3: 22 feet
Step-by-step explanation:
Side 1 is twice the length of side 2 and side 2 is 20 feet, which means side 1 is 40 feet. Side 3 is the the length of the second side plus 2, which means it has a length of 22 feet.
how many types of progression in mathematics?
Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 6 p plus 3 x plus 2 pxequals69. Suppose also that p and x are both functions of time, measured in days. Find the rate at which x is changing when xequals3, pequals5, and StartFraction dp Over dt EndFraction equals1.5.
Answer:
[tex]\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
Step-by-step explanation:
The price p, in dollars, and the number of sales, x, of a certain item follow the equation: 6p+3x+2px=69
Taking the derivative of the equation with respect to time, we obtain:
[tex]6\dfrac{dp}{dt} +3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}+2x\dfrac{dp}{dt}=0\\$Rearranging$\\6\dfrac{dp}{dt}+2x\dfrac{dp}{dt}+3\dfrac{dx}{dt}+2p\dfrac{dx}{dt}=0\\\\(6+2x)\dfrac{dp}{dt}+(3+2p)\dfrac{dx}{dt}=0[/tex]
When x=3, p=5 and [tex]\dfrac{dp}{dt}=1.5[/tex]
[tex](6+2(3))(1.5)+(3+2(5))\dfrac{dx}{dt}=0\\(6+6)(1.5)+(3+10)\dfrac{dx}{dt}=0\\18+13\dfrac{dx}{dt}=0\\13\dfrac{dx}{dt}=-18\\\dfrac{dx}{dt}=-\dfrac{18}{13}\\\\\dfrac{dx}{dt}=-1.3846$ sales per day[/tex]
The number of sales, x is decreasing at a rate of 1.3846 sales per day.
whats 1 and 1/2 + 2 and 3/10
Answer:
[tex]3\frac{4}{5}[/tex]
Step-by-step explanation:
You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.
10/10-->1
1/2--> 5/10
2--> 20/10
3/10, the denominator is already 10, so don't need to change.
10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]
Answer:
3 4/5
Step-by-step explanation:
hopefully this helped :3
Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.
Answer:
0.07
Step-by-step explanation:
The number of sophmores is 2+25+3 = 30.
Of these sophmores, 2 drive to school.
So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.
Answer:
[tex]\large \boxed{0.07}[/tex]
Step-by-step explanation:
The usual question is, "What is the probability of A, given B?"
They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"
We must first complete your frequency table by calculating the totals for each row and column.
The table shows that there are 30 students, two of whom drive to school.
[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]
Which value of x makes 7+5(x-3)=227+5(x−3)=227, plus, 5, left parenthesis, x, minus, 3, right parenthesis, equals, 22 a true statement? Choose 1 answer:
Answer:
7 + 5(x - 3) = 22
5(x - 3) = 15
x - 3 = 3
x = 6
Answer:
x = 6
Step-by-step explanation:
Step 1: Distribute 5
7 + 5x - 15 = 22
Step 2: Combine like terms
5x - 8 = 22
Step 3: Add 8 to both sides
5x = 30
Step 4: Divide both sides by 5
x = 6
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = (b) Find an expression for the number of cells after t hours. P(t) = (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr
Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
[tex]P(t)=Ce^{kt}[/tex]
For t=0, we have:
[tex]P(0)=Ce^0=C=58[/tex]
If we use the duplication time, we have:
[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]
Then, we have the model as:
[tex]P(t)=58e^{2.08t}[/tex]
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]
The rate of growth can be calculated as dP/dt and is:
[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]
For t=8, the rate of growth is:
[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as:
[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]
find the LCM and solve, it's very very urgent.
Answers:
1. 10502. 12003. 12004. 33605. 10806. 480please see the attached picture for full solution..
Hope it helps....
Good luck on your assignment...
If 2x+9<32 then x could be
Answer:
x < 11.5
Step-by-step explanation:
2x + 9 < 32
(2x + 9) - 9 < 32 - 9
2x < 23
2x/2 < 23/2
x < 11.5
Answer:
x < 11 1/2
Step-by-step explanation:
2x+9<32
Subtract 9 from each side
2x+9-9 < 32-9
2x<23
Divide by 2
2x/2 <23/2
x < 11 1/2
X is any number less than 11 1/2
Which of the following graphs is described by the function given below?
y = 2x^2 + 8x + 3
Answer:
Option A
Step-by-step explanation:
Equation of the given quadratic function is,
y = 2x² + 8x + 3
y = 2(x² + 4x) + 3
= 2(x² + 4x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
By comparing this equation with the equation of a quadratic function in vertex form,
y = a(x - h)² + k
Here (h, k) is the vertex of the parabola
Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)
Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.
Option (A). Graph A will be the answer.
Select the correct answer.
If two angles of a triangle have equal measures and the third angle measures 90º, what are the angle measures of the triangle?
ОА.
60°, 60°, 60°
OB.
459,909, 90°
Ос.
30°, 30°, 90°
OD.
45°, 45°, 90°
Answer:
OD. 45,45,90
Step-by-step explanation:
Which set of numbers can represent the lengths of the sides of a triangle? A. {1,2,3} B. {3,5,7} C. {3,9,14} D. {4,4,8}
The set of numbers that can represent the lengths of the sides of a triangle are 3,5,7. That is option B.
What is a triangle?Triangle is defined as a type of polygon that has three sides in which the sum of both sides is greater than the third side.
That is to say, 3+5 = 8 is greater than the third side which is 7.
Therefore, the set of numbers the would represent a triangle are 3,5,7.
Learn more about triangle here:
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15% as a fraction in its lowest terms is:
-3/20
-5/100
-1/15
-3/100
Answer:
3/20
Step-by-step explanation:
15%
15/100
/5 /5
3/20
which equation represents the graph function?
Answer:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
Step-by-step explanation:
First, notice that since the graph of the function is a line, we have a linear function.
To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We are given the point (0,3) which is the y-intercept. Thus, b = 3.
To find the slope, we can use the slope formula:
[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]
Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]
objective: Solve applications involving problem-s...
1 of 21 (0
1.1.A-4
Cookies are sold singly or in packages of 8 or 24. With this packaging, how many
ways can you buy 48 cookies?
Step-by-step explanation:
With the packaging of 8
48 cookies = 48 ÷ 8 = 6 boxes
With the packaging of 24
48 cookies = 48 ÷ 24 = 2 boxes
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 58.2 σ=58.2. You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.
Answer:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Step-by-step explanation:
Let's define some notation
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=58.2[/tex] represent the population standard deviation
n represent the sample size
[tex] ME =1[/tex] represent the margin of error desire
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be [tex]\alpha=0.01[/tex] and the critical value [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547[/tex]
So the answer for this case would be n=22547 rounded up to the nearest integer
Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3
Answer:
99% confidence interval for the mean of college students
A) 112.48 < μ < 117.52
Step-by-step explanation:
step(i):-
Given sample size 'n' =150
mean of the sample = 115
Standard deviation of the sample = 10
99% confidence interval for the mean of college students are determined by
[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]
Step(ii):-
Degrees of freedom
ν = n-1 = 150-1 =149
t₁₄₉,₀.₀₁ = 2.8494
99% confidence interval for the mean of college students are determined by
[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]
on calculation , we get
(115 - 2.326 , 115 +2.326 )
(112.67 , 117.326)
Will anyone help me with geometry ASAP!? Please!? In desperate help!!!
Answer:
14. C 41
15. k = 72
Step-by-step explanation:
14.
For parallel lines, alternate exterior angles must be congruent.
3x - 43 = 80
3x = 123
x = 41
15.
The sum of the measures of the angles of a triangle is 180 deg.
k + 33 + 75 = 180
k + 108 = 180
k = 72
Answer:
1. 32
2. 41
3. 72
Step-by-step explanation:
The area of a rectangular horse pasture is 268,500 square yards. The length of the pasture is 5 yards less than three times the width. What is the width of the pasture in yards? Do not include units in your answer. Please help right away! Thank you very much!
Answer: width = 300
Step-by-step explanation:
Area (A) = Length (L) x width (w)
Given: A = 268,500
L = 3w - 5
w = w
268,500 = (3w - 5) x (w)
268,500 = 3w² - 5w
0 = 3w² - 5w - 268,500
0 = (3w + 895) (w - 300)
0 = 3w + 895 0 = w - 300
-985/3 = w 300 = w
Since width cannot be negative, disregard w = -985/3
So the only valid answer is: w = 300
Find the area of this parallelogram.
6 cm
11 cm
Step-by-step explanation:
given,
base( b) = 6cm
height (h)= 11cm
now, area of parallelogram (a)= b×h
or, a = 6cm ×11cm
therefore the area of parallelogram (p) is 66cm^2.
hope it helps...
Alexandra has $15 to buy drinks for her friends at the baseball game. Soda
costs $2.75 and bottled water costs $2.00. This relationship can be
represented by the inequality 2758+2w $ 15. Three of Alexandra's friends
asked for water. Which inequality represents the number of sodas she can
buy?
A. OS 85 3.27
B. 85 3.27
C. OSSS3
D. 853
Answer:
C
Step-by-step explanation:
write an equation for the costs:
if x is the number of sodas
and y is the number of waters
2.75x + 2y <= 15
(<= is less than or equal to)
if we substitute 3 for y
we get 2.75x + 2(3) <= 15
2.75x + 6 <= 15
2.75x <= 9
9 / 2.75 = 3.2727
however, you cannot buy part of a soda
so, round to 3
you also cannot buy negative sodas
so, the answer is C
In a particular year, the mean score on the ACT test was 19.6 and the standard deviation was 5.2. The mean score on the SAT mathematics test was 546 and the standard deviation was 126. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal placesFind the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is ______ .
Answer:
0.11
Step-by-step explanation:
Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2
By comparing P(0≤ Z ≤ 26)
P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)
= P(Z ≤ 1.231)
Using Table: P(0 ≤ Z ≤ 1) = 0.39
P(Z > 1) = (0.5 - 0.39) = 0.11
∴ P(Z > 26) = 0.11
At her favorite sneakers store Nyeema saved $48 because of a
sale.
If the sneakers normally cost $120. How much did she save?
Answer:
40%
Step-by-step explanation:
We can find what percent 48 is of 120 by dividing:
48/120 = 0.4 or 40%
So, she saved 40% from the original price.
Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.
Answer:
With replacement = 14/49without replacement = 3/7Step-by-step explanation:
Since there are 2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.
Probability that at least 1 ball was red, given that the first ball was replaced before the second can be calculated as shown;
Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.
Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49
Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49
The probability that at least 1 ball was red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49
If the balls were not replaced before the second draw
Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21
Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21
The probability that at least 1 ball was red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7
The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:
2 + 5 = X7 = X
(2/7 + 2/7) / 2 = X (0.285 + 0.285) / 2 = X 0.285 = X
(2/7 + 1/6) / 2 = X (0.28 + 0.16) / 2 = X 0.451 / 2 = X 0.225 = X
Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.
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Factor the trinomial!! PLEASE HELP and if possible please explain how to do this!!
Answer:
d. a = 39
Step-by-step explanation:
Question:
for which value of "a" will the trinomial be factorizable.
x^2+ax-40
For the expression to have integer factors, a = sum of the pairs of factors of -40.
-40 has following pairs of factors
{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }
meaning that the possible values of a are
+/- 39, +/- 18, +/- 6, +/- 3
out of which only +39 appears on answer d. a=39
compute the missing data in the table for the following exponential function f(x)={1/4}
Answer:
1/256
Step-by-step explanation:
The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.