Answer:
A) Brown-Brown ,Brown-Blue, Blue-Brown, Blue-Blue B) 1/4 =0,25 C)3/4=0,75
Step-by-step explanation:
Lets mother's "BROWN" is "BROWN-M",
mother's "BLUE" is " BLUE-M"
Lets father's "BROWN" is "BROWN-F" and
father's "BLUE " is "BLUE-F"
The kid can have the genotype as follows (list of possible outcomes) :
1. BROWN-M>BROWN-F ( received BROWN as from mother as from father)
2. BROWN-M>BLUE-F ( Received BROWN from mother and BLUE from father)
3. BLUE-M>BROWN-F ( Received BLUE from mother and Brown from father)
4. BLUE-M>BLUE-F ( Received BLUE as from mother as from father)
b) As we can see in a) only 1 outcome from 4 is BLUE-BLUE. So the probability of BLUE-BLUE genotype is
P(BLUE>BLUE)=1/4=0.25
c) As we know that if the child has at least one brown allele, that color will dominate and the eyes will be brown.
It means that outcomes BROWN-BROWN, BROWN-BLUE and BLUE-BROWN determine brown color of eye. So the number of these outcomes is 3. Total amount of outcomes is 4.
So probability that eyes are brown is P(Brown eyes)=3/4 =0.75
What is the value of x?
Enter your answer in the box.
Answer:
x=11
Step-by-step explanation:
Since the lines in the middle are parallel, we know that both sides are proportional to each other.
6:48 can be simplified to 1:8
Since we know the left side ratio is 1:8, we need to match the right side with the same ratio
We can multiply the ratio by 5 to match 5:3x+7
5:40
5:3x+7
Now we can set up the equation: 40=3x+7
Subtract 7 from both sides
3x=33
x=11
When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 550 USD can be converted into 24,334.75 PHP.
Find the constant of proportionality k.
k= ______ (If needed, round answer to 3 decimal places.)
Using the k from above find the amount of PHP given that you have 900 USD to convert. You will receive ________ PHP (If needed, round answer to 2 decimal places.)
Answer:
(a)k=44.245
(b)39820.50 PHP
Step-by-step explanation:
Part A
Let the number of PHP =y
Let the number of USD =x
The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.
The equation of proportion is: y=kx
If 550 USD can be converted into 24,334.75 PHP.
x=550y=24,334.75Substitution into y=kx gives:
[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]
The constant of proportionality k=44.245
Part B
The equation connecting y and x then becomes:
y=44.245x
If x=900 USD
Then:
y=44.245 X 900
y= 39820.50
Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP
what is the volume of a cone with a radius of 3 and a height of 17
━━━━━━━☆☆━━━━━━━
▹ Answer
V ≈ 160.22
▹ Step-by-Step Explanation
V = πr²[tex]\frac{h}{3}[/tex]
V = π3²[tex]\frac{17}{3}[/tex]
V ≈ 160.22
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Which equation represents a line that passes through (2,-2) and has a slope of 3?
y-2 = 3(x +
y – 3 = 2(x + ?)
y +
= 3(x - 2)
y +
= 2(x - 3)
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1) Choices: a. g(x) has to be: (1+x)/2 b. g(x) has to be: x/2 c. g(x) has to be: 2 – (1/x) d. Inverses
Answer:
(f o g) = x, then, g(x) is the inverse of f(x).
Step-by-step explanation:
You have the following functions:
[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]
In order to know if f and g are inverse functions you calculate (f o g) and (g o f):
[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]
[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]
(f o g) = x, then, g(x) is the inverse of f(x).
What’s the probability of getting each card out of a deck?
Determine the probability of drawing the card(s) at random from a well-shuffled regular deck of 52 playing cards.
a. a seven __________
b. a six of clubs. ___________
c. a five or a queen ___________
d. a black card. ___________
e. a red card or a jack. ___________
f. a club or an ace. ___________
g. a diamond or a spade. ___________
Answer:
a. 1/13
b. 1/52
c. 2/13
d. 1/2
e. 15/26
f. 17/52
g. 1/2
Step-by-step explanation:
a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:
P(7) = 4/52 = 1/13
b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:
P(6 of clubs) = 1/52
c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen is:
P(5 or Q) = P(5) + P(Q)
= 4/52 + 4/52
= 1/13 + 1/13
P(5 or Q) = 2/13
d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:
P(B) = 26/52 = 1/2
e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:
P(R or J) = P(R) + P(J)
= 26/52 + 4/52
= 30/52
P(R or J) = 15/26
f. There are 13 cards in clubs suit and there are 4 aces, therefore:
P(C or A) = P(C) + P(A)
= 13/52 + 4/52
P(C or A) = 17/52
g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:
P(D or S) = P(D) + P(S)
= 13/52 + 13/52
= 26/52
P(D or S) = 1/2
State the coordinates of the vertex for each of the following
Answer:
[a] y=x^2+3, vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
[d] y= (1/2)x^2 - 5, vertex, V(0,-5)
Step-by-step explanation:
The vertex, V, of a quadratic can be found as follows:
1. find the x-coordinate, x0, by completing the square
2. find the y-coordinate, y0, by substituting the x-value of the vertex.
[a] y=x^2+3, vertex, V(0,3)
y=(x-0)^2 + 3
x0=0, y0=0^2+3=3
vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
y=2(x-0)^2+0
x0 = 0, y0=0^2 + 0 = 0
vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
y=-(x^2-0)^2 + 4
x0 = 0, y0 = 0^2 + 4 = 4
vertex, V(0,4)
y = (1/2)(x-0)^2 -5
x0 = 0, y0=(1/2)0^2 -5 = -5
vertex, V(0,-5)
Conclusion:
When the linear term (term in x) is absent, the vertex is at (0,k)
where k is the constant term.
I NEED HELP PLEASE, THANKS!
Answer:
the 3rd option is the answer
Step-by-step explanation:
I hope the attached file is self-explanatory
Which comparison is correct?
0.298 < 0.289
0.420 > 0.42
1.32 < 1.319
d) 3.544 > 3.455
Step-by-step explanation:
Option D is the correct answer because 3.544 is greater than 3.455
Option D is true in given comparison.
Here,
We have to find the correct comparison.
What is Decimal expansion?
The decimal expansion terminates or ends after finite numbers of steps. Such types of decimal expansion are called terminating decimals.
Now,
In option D;
The one tenth of 3.544 is 5 and place value of one tenth number in 3.455 is 4.
Clearly, 5 > 4
So, 3.544 > 3.455
Hence, option D; 3.544 > 3.455 is true.
Learn more about the Decimal expansion visit:
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A daffodil grows 0.05m every day. Plot the growth of the flower if the initial length of the daffodil is 0.8m and hence give the length of the daffodil on the 8th day.
Answer:
1.2m
Step-by-step explanation:
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
Hope this helps you out! : )
the length of the daffodil on the 8th day is 1.2m.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
A daffodil grows 0.05m every day.
the initial length of the daffodil is 0.8m.
You must first find out how much the daffodil grew over the 8 days:
0.05 x 8 = 0.4
Then you must add how much it grew to the original height:
0.4 + 0.8 = 1.2
hence, the length of the daffodil on the 8th day is 1.2m.
To learn more on multiplication click:
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The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Suppose that 43 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(_______,_________)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(______,_________)
If a single randomly selected individual is observed, find the probability that this person consumes is between 61.4 mL and 62.8 mL. ________
For the group of 43 pancake eaters, find the probability that the average amount of syrup is between 61.4 mL and 62.8 mL. _________
For part d), is the assumption that the distribution is normal necessary? No Yes
please only answer if you are able to answer all parts correctly
Answer:
(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
[tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Step-by-step explanation:
We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.
Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.
(a) Let X = amount of syrup that people put on their pancakes
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
n = sample of people = 43
So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)
P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)
P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)
= 1 - 0.50798 = 0.49202
P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)
= 1 - 0.54776 = 0.45224
Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)
P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)
P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)
= 1 - 0.53983 = 0.46017
P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)
= 1 - 0.79103 = 0.20897
Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal
Answer:
$904,510.28
Step-by-step explanation:
If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.
P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)
where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.
Filling in your values, we have ...
P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)
P = $904,510.28
You need to have $904,510.28 in your account when you begin withdrawals.
Answer:
You need to have $904,510.28 in your account when you begin
Plz. Can anyone explain and tell the answer of this question.I promise I will mark it as brainliest Question.
Answer:
x = 15
y = 90
Step-by-step explanation:
Step 1: Find x
We use Definition of Supplementary Angles
9x + 3x = 180
12x = 180
x = 15
Step 2: Find y
All angles in a triangle add up to 180°
3(15) + 3(15) + y = 180
45 + 45 + y = 180
90 + y = 180
y = 90°
The scientist performs additional analyses and observes that the number of major earthquakes does appear to be decreasing but wonders whether the relationship is statistically significant. Based on the partial regression output below and a 5% significance level, is the year statistically significant in determining the number of earthquakes above magnitude 7.0?Dependent Variable: Earthquakes above Magnitude 7.0 Coefficients Standard t Stat P-value Lower 95% Upper 95% ErrorIntercept 64.67 38.08 4.32 89.22 240.12Year -0.07 0.02 -3.82 -0.11 -0.04
Answer:
Step-by-step explanation:
Hello!
A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.
^Y= 164.67 - 0.07Xi
Y: earthquake above magnitude 7.0
X: year
The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0
The hypotheses are:
H₀: β = 0
H₁: β ≠ 0
α: 0.05
The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]
The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]
This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.
The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:
p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]
As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.
If you want to use the rejection region approach, the sample size is also needed to determine the critical values.
But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.
Using the CI, the decision rule is as follows:
If the CI includes the "zero", do not reject the null hypothesis.
If the CI doesn't include the "zero", reject the null hypothesis.
The calculated interval for the slope is: [-0.11; -0.04]
As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.
At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.
I hope this helps!
(full output in attachment)
Still timed. More math needing help with, i'll double points and mark brainliest! 1. (y - 6) (y + 3) 2. (4x - 5) (x - 7) 3.(3x - 2) ( 4x - 1)
Answer:
1. y² - 3x - 18
2. 4x² - 33x + 35
3. 12x² - 11x + 2
Step-by-step explanation:
All we do with these questions are expanding the factored binomials. Use FOIL:
1. y² + 3y - 6y - 18
y² - 3y - 18
2. 4x² - 28x - 5x + 35
4x² - 33x + 35
3. 12x² - 3x - 8x + 2
12x² - 11x + 2
Answer:
1) (y-6) (y+3)
=> [tex]y^2+3y-6y-18[/tex]
=> [tex]y^2-3y-18[/tex]
2) (4x-5) (x-7)
=> [tex]4x^2-28x-5x+35[/tex]
=> [tex]4x^2-33x+35[/tex]
3) (3x - 2) ( 4x - 1)
=> [tex]12x^2-3x-8x+3[/tex]
=> [tex]12x^2-11x+3[/tex]
The nth term of a geometric sequence is given by an = 27(0.1)n - 1. Write the first five terms of this sequence.
Answer:
The first first five terms of this sequence are
27 ,2.7 ,0.27 ,0.027 , 0.0027Step-by-step explanation:
[tex]a(n) = 27(0.1)^{n - 1} [/tex]
where n is the number of term
For the first term
n = 1
[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]
= 27(1)
= 27Second term
n = 2
[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]
= 27(0.1)
= 2.7Third term
n = 3
[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]
= 0.27Fourth term
n = 4
[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]
= 0.027Fifth term
n = 5
[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]
= 0.0027Hope this helps you
Which monomial is a perfect cube? I I A 1x3 B 3x3 C 6x3 D 9x3
Answer:
option D 9x³
Step-by-step explanation:
the monomial 9x³ comes from (3x)³, which gives, 3×3×3×x×x×x= 9x³
9 is 3 times 3 and x³ is 3 times x. So here, 9x³ is a perfect cube
Make sure you answer this 100% correctly
Answer:
A
Step-by-step explanation:
f(x) = x² + 3x + 5
Substitute x value with (a+ h)
f(a+h) = (a+h)² + 3(a+h) + 5
= a² +2ah +h² + 3a + 3h + 5
Which best describes the circumference of a circle?
Answer: A
Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
Amanda is constructing equilateral triangle JKL inscribed in circle M. To construct the inscribed polygon, she is going to use a compass to partition the circle into congruent arcs. To what width should she set the compass when partitioning the circle? A. The width must be equal to the radius of circle M. B. The width must be equal the diameter of circle M. C. The width can be equal to either the radius or the diameter of circle M. D. The width can be any size greater than the radius but less than the diameter of circle M. E. The width must be less than the radius of circle M. help meee please!!!!!!!!!!!!!!!!!
Given:
An equilateral triangle JKL inscribed in circle M.
Solution:
To draw an equilateral triangle inscribed in circle follow the steps:
1: Draw a circle with any radius.
2. Take any point A, anywhere on the circumference of the circle.
3. Place the compass on point A, and swing a small arc crossing the circumference of the circle.
Remember the span of the compass should be the same as the radius of the circle.
4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.
5. Repeat this process until you return to point A.
6. Join the intersecting points on the circle to form the equilateral triangle.
So the correct option is A. The width must be equal to the radius of circle M.
A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answer:
The integers are 7 and 14.
Step-by-step explanation:
y = 2x
1/y + 1/x = 3/14
1/(2x) + 1/x 3/14
1/(2x) + 2/(2x) = 3/14
3/(2x) = 3/14
1/2x = 1/14
2x = 14
x = 7
y = 2x = 2(7) = 14
Answer: The integers are 7 and 14.
The required two integers are 7 and 14
This is a question on word problems leading to the simultaneous equation:
Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1
Also, if the sum of the reciprocals of the two positive integers is 3/14, then:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2
Substitute equation 1 into 2
[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]
Find the LCM of 2y and y
[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]
Substitute y = 7 into equation 1:
Recall that x = 2y
[tex]x = 2(7)\\x = 14[/tex]
Hence the required two integers are 7 and 14.
Learn more here: https://brainly.com/question/17671977
Can somebody help me with this question
In a random sample of 2,305 college students, 339 reported getting 8 or more hours of sleep per night. Create a 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answer:
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
The angles in a triangle are such that one angle is 30 degrees more than the smallest angle while the third angle is four times as large as the smallest angle find the measure are of all three angles
Answer:
25, 55, 100
Step-by-step explanation:
Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:
x + x + 30 + 4x = 180
6x + 30 = 180
6x = 150
x = 25°
x + 30 = 25 + 30 = 55°
4x = 25 * 4 = 100°
The sum of angles is 180.
[tex] \alpha + \beta + \gamma = 180 [/tex]
[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]
[tex]6 \alpha = 150[/tex]
[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]
Hippocrates magazine states that 32 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 261 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level?
Select the [p-value, Decision to Reject (RHo) or Failure to Reject (FRHo)1.
a) [p-value = 0.069, FRHI
b) [p-value = 0.009, RH01
c) [p-value = 0.009, FRHol
d) [p-value = 0.019, FRH)]
e) [p-value = 0.019, RHo]
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.32
For the alternative hypothesis,
p ≠ 0.32
This is a two tailed test
Considering the population proportion, probability of success, p = 0.32
q = probability of failure = 1 - p
q = 1 - 0.32 = 0.68
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 261
n = number of samples = 750
P = 261/750 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8
Recall, population proportion, p = 0.32
The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29
the p for the right tail is 0.32 + 0.03 = 0.35
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359
We would double this area to include the area in the right tail of z = 0.44 Thus
p = 0.0359 × 2 = 0.07
Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.
A triangle has sides of lengths 9, 7, and 12. Is it a right triangle? Explain.
Answer:
Yes based on the numbers .
Step-by-step explanation:
Answer:Yes
Step-by-step explanation:Based on the number given, it shows that there is a hypotenuse (The longest side of a right triangle, in this case being 12), And opposite (Another part of the right triangle, that could be either 9 or 7), and the adjacent (The line next to the opposite, which could be 9 or 7)
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. Click on the datafile logo to reference the data. 6 4 6 8 7 7 6 3 3 8 10 4 8 7 8 7 5 9 5 8 4 3 8 5 5 4 4 4 8 4 5 6 2 5 9 9 8 4 8 9 9 5 9 7 8 3 10 8 9 6Develop a 95% confidence interval estimate of the population mean rating for Miami.
Answer:
The 95% confidence interval for the population mean rating is (5.73, 6.95).
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=6.34.
The sample size is N=50.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]
The 95% confidence interval for the mean is (5.73, 6.95).
is a parallelogram sometimes always or never a trapezoid
yes
Step-by-step explanation:
parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.
Consider a comparison of two models. The "complete" model has both curvature and interaction. The "reduced" model has curvature, but no interaction. You compare the two models using a nested (subset) F-test and determine that you should "reject H0 ". True or False: The reduced model fits the data better than the complete model. Group of answer choicesTrueFalse
Answer:
True
Step-by-step explanation:
The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.