Answer: The area is 9π unit squared ( in terms of π)
Step-by-step explanation:
From the equation for area of a circle, A = πr²
Where A is the area of the circle
r is the radius of the circle
From the question, the radius, r of the circle is 3
r = 3
Therefore, the Area of the circle is given by
A = π × (3)²
A = π×3×3
A = 9π unit squared ( in terms of π)
Hence, the area is 9π unit squared
OR
Since π is given as 3.14
Then,
A = 3.14 × (3)²
A = 3.14 × 3 × 3
A = 28.26 unit squared
Hence, Area is 28.26 unit squared (in decimal)
PLEASE HURRY In order to solve the system of equations below, Juana multiplies each equation by a constant to eliminate the y terms.
4x-3y = 1
5x+4y=9
What are the resulting equations?
16x-12y - 4
15x+12y - 27
16x-12y=-4
15x+12y = 27
16x-12y=-4
15x-12y = 27
Answer:
16x -12y = 4
15x +12y = 27
Step-by-step explanation:
4x-3y = 1
5x+4y=9
We will use elimination to remove y from both equations.
We can multiply the first equation by 4
16x -12y = 4
and multiply the second equation by 3
15x +12y = 27
This will eliminate y from the system of equations, leaving only x as a variable.
Answer:
16x - 12y = 4
15x + 12y = 27
Step-by-step explanation:
In order to eliminate the y terms, the equations must be manipulated in order to make the coefficient of the y-term equal 0 when the equations are added.
In this case, we are trying to make one equation with -3y and another equation with 4y result in a single equation with 0y.
We can do this by multiplying the first equation by 4 and the second equation by 3 to result in -12y and 12y. When these are added, the sum is 0y.
4 * (4x - 3y = 1) = 16x - 12y = 4
3 * (5x + 4y = 9) = 15x + 12y = 27
The resulting equations are
16x - 12y = 4
15x + 12y = 27
Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.
Answer:
4.5 inches
Step-by-step explanation:
Put the given values in the volume formula and solve for width:
V = LHW
138.24 = (3.2)(9.6)W
138.24/30.72 = W = 4.5
The width of the prism is 4.5 inches.
#18 *
C) Assessment Practice
18. Last month you spent $30. This month you spent 140% of what you spent
last month. Set up a proportion to model this situation. How much did you
spend this month?
Your answer
Answer: You spent $42 this month.
Step-by-step explanation:
[tex]\frac{x}{30} = \frac{140}{100}[/tex] solve by cross product
100x = 4200
x= 42
The data below are the frequency of cremation burials found in 17 archaeological sites. a. Obtain the mean, median, and mode of these data. b. Which measure of center do you think works best here? 85 67 45 47 524 32 31 272 2141 45 390 28 86 424 59 256 143 a. The mean is 275. (Round to one decimal place as needed.) The median is nothing. (Round to one decimal place as needed.) Select the correct choice below and fill in any answer boxes within your choice. A. The mode is nothing. (Round to one decimal place as needed.) B. There is no mode. b. Which measure of center works best here?
Answer:
(a) The mean of the data is 275.
(b) The median of the data is 85.
(c) The mode of the data is 45.
(d) The measure of center that works best here will be median.
Step-by-step explanation:
We are given below the frequency of cremation burials found in 17 archaeological sites. Arranging those in ascending order we get;
28, 31, 32, 45, 45, 47, 59, 67, 85, 86, 143, 256, 272, 390, 424, 524, 2141.
(a) The formula for calculating mean for the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{28+ 31+ 32+ 45+ 45+ 47+ 59+ 67+ 85+ 86+ 143+ 256+ 272+ 390+ 424+ 524+ 2141}{17}[/tex]
= [tex]\frac{4675}{17}[/tex] = 275
So, the mean of the data is 275.
(b) Since, the number of observations (n) in our data is odd (i.e. n = 17) , so the formula for calculating median is given by;
Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{17+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{18}{2} )^{th} \text{ obs.}[/tex]
= [tex]9^{th} \text{ obs.}[/tex] = 85
So, the median of the data is 85.
(c) Mode is that value in our data which appears maximum number of times in our data.
So, after observing our data we can see that only number 45 is appearing maximum number of times (2 times) and all other numbers are appearing only once.
So, the mode of the data is 45.
(d) The measure of center that works best here will be median because there are outliers in our data (means extreme values) and mean gets affected by the outliers.
So, the best measure would be median as it represents the middle most value of our data.
Can someone tell me what 58-(1/4)^2 is
Answer:
57.9375
Step-by-step explanation:
Answer:
The answer above this is correct
n a recent awards ceremony, the age of the winner for best actor was 35 and the age of the winner for best actress was 48. For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years. For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.
Answer:
The best actor's age is farther from the mean, so he has the more extreme age when winning the award
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whichever z-score's has the highest absolute value, that is, is farther from the mean, has the most extreme age.
Best actor:
Age of 35, so [tex]X = 35[/tex].
For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years, so [tex]\mu = 48.7, \sigma = 8.9[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 48.7}{8.9}[/tex]
[tex]Z = -1.54[/tex]
Best actrees:
Age of 48, so [tex]X = 48[/tex]
For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so [tex]\mu = 34.7, \sigma = 11.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 34.7}{11.7}[/tex]
[tex]Z = 1.14[/tex]
The best actor's age is farther from the mean, so he has the more extreme age when winning the award
Find the length of OX
start overline, O, X, end overline.
If entering your answer as a decimal, round your final answer to the nearest hundredth
Answer:
Length OX = 7.09 units
Step-by-step explanation:
The diagram of the full question is attached to this solution.
Let the length of OX be x
Then length of OD = (13 - x)
From the image of the figure, it is given that
Angle BOL = Angle LOP
Let that angle be equal to θ
Angle BOL = Angle LOP = θ
But since lines BX, OL and PD are evidently parallel to one another, we can say that
Angle OPD = Angle LOP = θ (alternate angles are equal)
Also, Angle OBX = Angle BOL = θ (alternate angles are equal)
And from trigonometric relations,
Sin θ = (x/12)
And
Sin θ = (13 - x)/10
Since sin θ = sin θ
We can then equate
(x/12) = (13 - x)/10
cross multiplying
10x = 12 (13 - x)
10x = 156 - 12x
10x + 12x = 156
22x = 156
x = (156/22) = 7.091 = 7.09 to the nearest hundredth.
Hence, length OX = 7.09 units
Hope this Helps!!!
Answer: 7.09
Step-by-step explanation:
i got this answer from AyBaba7 and khan. thank you AyBaba7!!!!! :)
Gary drew a rectangle with a perimeter of 12 inches. Then he tried to draw a square with a pe
of 12 inches
Select the dimensions of the rectangle drawing.
1 inch by 5 inches
12 inches by 5 inches
5 inches by 3 inches
12 inches by 1 inch
Select the dimensions of the square drawing.
5 inches by 5 inches
1 inch by 1 inch
3 inches by 3 inches
12 inches by 12 inches
Answer:
A. 1 inch by 5 inches
B. 3 inches by 3 inches
Step-by-step explanation:
The perimeter of a rectangle is the sum of the sides of the rectangle. The perimeter of a rectangle can be represented mathematically as
perimeter of a rectangle = 2l + 2w
where
l = length
w = width
perimeter = 12 inches
perimeter of a rectangle = 2l + 2w
12 = 2(l + w)
divide both sides by 2
l + w = 12/2
l + w = 6
Base on the option the dimension can only be 1 inches by 5 inches because the sum can give 6.
Square
The perimeter of the square is 12 inches.
perimeter of a square = 4l
where
l = length
12 = 4l
divide both sides by 4
l = 12/4
l = 3 inches
The length should be 3 inches by 3 inches.
3 more than the cube of a number.
Answer:
x³+3
Step-by-step explanation:
Answer:
x³+3
Step-by-step explanation:
x³+3
Twelve bears eat five pounds of honey in one day. At the same rate, how many pounds of honey will 20 bears eat in three days?
Answer:
25
Step-by-step explanation:
Want Brainliest? Get this correct , What is the equation of this function after it is reflected over the y-axis?
Answer:
(-x+4)^3
Step-by-step explanation:
when you turn the x to negtive it filps over the y-axis and if the whole thing is negitve like -(x+4)^3 it filps over the x-axis
jus took the test. Your answer is F(x)=-(x+4)^3
A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Answer:
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
54% of the school's graduates move to a different state after graduating.
This means that [tex]p = 0.54[/tex]
7 randomly selected graduates
This means that [tex]n = 7[/tex]
Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Either none moves, or at least one does. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]. Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.54)^{0}.(0.46)^{7} = 0.0044[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0044 = 0.9956[/tex]
99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.
Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gallons of heating oil. What fraction of the tank's total capacity will be full in 30 minutes?
Answer:
5/8
Step-by-step explanation:
The volume after 30 minutes is:
(4.5 gal/min) (30 min) + 115 gal = 250 gal
The fraction of total capacity is:
250 gal / 400 gal = 5/8
The fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Heating oil is to be poured at the constant rate of 4.5 gallons (17.03 l) per minute into a 400-gallon tank that already contains 115 gallons (435.32 l) of heating oil.
Then the fraction of the tank's total capacity will be full in 30 minutes will be
The amount of oil in the tank after 30 minutes. Then we have
Amount of oil in the tank = 115 + 4.5 x 30
Amount of oil in the tank = 115 + 135
Amount of oil in the tank = 250 gallons (946.35 l)
Then the fraction of the tank's total capacity will be full in 30 minutes will be
⇒ 250 / 400
⇒ 5 / 8
Thus, the fraction of the tank's total capacity will be full in 30 minutes will be 5 / 8.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
What is the lowest value of the range of the function shown on the graph? 0 3
Answer:
-2
Step-by-step explanation:
Edge 2020
Answer: B. -2
Step-by-step explanation: On Edge!!!!!
Suppose tortilla chips cost 22.5 cents per ounce. If a bag costs $3.07, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answer:
13.64 ounces
Step-by-step explanation:
Cost per ounce = $0.225
Cost per bag = $3.07
The number of ounces in a bag of chips is given by the cost per bag divided by the cost per ounce:
[tex]n=\frac{3.07}{0.225}\\ n=13.64\ ounces[/tex]
There are 13.64 ounces in a bag of chips.
When will n(A∩B)=0? Explain and give an example.
Answer:
Two sets are called disjoint if they have no elements in common. For example:
The sets S = { 2, 4, 6, 8 } and T = { 1, 3, 5, 7 } are disjoint.
Another way to define disjoint sets is to say that their intersection is the empty set,
Two sets A and B are disjoint if A ∩ B = 0.
In the example above,
S ∩ T = ∅ because no number lies in both sets.
Step-by-step explanation:
When two sets A and B having no common items then n(A∩B) = 0.
What are disjoint sets?In mathematics, two sets are said to be disjoint sets if they have no element in common.
Let there be two sets A and B,
A = {a, b, c, d}
B = {e, f, g, h}
Therefore intersection of A ad B we get,
A∩B = {0}
Thus, the number of elements in n(A∩B) is 0.
⇒ n(A∩B) = 0
Thus, when two sets A and B having no common items then n(A∩B) = 0.
To learn more about sets :
https://brainly.com/question/6460554
#SPJ2
subtract the sum of -1250 and 1138 from the sum of 1136 and 1272
Answer:
2528
Step-by-step explanation:
-1250+1130=-120
1136+1272=2408
2408-(-120)=2528
hope it helps
The depth of water at the end of a pier varies with the tides. The low tides occur on a particular day at 2:00 a.m. and 2:00 p.m. with a depth of 1.1 m. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 5.3 m. A large boat needs at least 3 m of water to be safely secured at the end of the pier. What is the first time in the morning that is it safe for the boat to be tied to the pier
Answer:
4:42 a.m.
Step-by-step explanation:
The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.
Between these hours, 6 hours elapsed.
The lowest point is 1.1 m and increases steadily to 5.3 m.
Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,
0 = 1.1 m
x = 3 m
6 = 5.3 m
we solve as [tex]\frac{x - 0}{6 - 0}[/tex] = [tex]\frac{3 - 1.1}{5.3 - 1.1}[/tex]
[tex]\frac{x}{6}[/tex] = [tex]\frac{1.9}{4.2}[/tex]
4.2x = 11.4
x = 2.71 hours from 2:00 a.m.
= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min
the time will approximately be by 4:42 a.m.
A researcher wants to investigate whether there is a relationship between annual company profit ($) and median annual salary paid by the company ($). The researcher collects data on a random sample of companies and after analyzing the data finds the p-value to be 0.56. Which of the following is an appropriate conclusion based on this p-value?A. There is a 56% chance that there is no relationship between annual company profit and median annual salary paid by the company.
B. There is a relationship between annual company profit and median annual salary paid by the company, and the corresponding value of the correlation coefficient is r = 0.56.
C. There is no relationship between annual company profit and median annual salary paid by the company.
D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.
Answer:
D. There is not convincing evidence of a relationship between annual company profit and median annual salary paid by the company.
Step-by-step explanation:
In this hypothesis test, the null hypothesis usually states that there is no relationship between the two variables in study.
In opposite, the claim that is being tested is the speculative hypothesis: that there is a significant relationship between both variables.
The researcher takes a sample and the P-value indicates the probability of getting that sample by pure chance if the null hypothesis is true.
Then, a very small P-value, below the significance level, indicates that the sample is very unusual if the null hypothesis is true, what gives evidence to reject the null hypothesis.
In this case, a P-value of 0.56 indicates that the sample is not unusual if the null hypothesis is true, so it gives no support to the claim that the null hypothesis is false and that there exists a relationship between the two variables in study.
D. There is not convincing evidence of a relationship between annual company profit and a median annual salary paid by the company.
An appropriate conclusion based on this p-value is that there is not convincing evidence of a relationship between annual company profit and the median annual salary paid by the company. The researcher takes a sample, and if the null hypothesis is true, the P-value indicates the probability of taking this sample purely by chance. A very small P-value below the significance level indicates that the sample is very abnormal if the null hypothesis is true. This indicates that the null hypothesis needs to be rejected. In this case, a P-value of 0.56 indicates that the sample is not uncommon if the null hypothesis is true. Therefore, the claim that the null hypothesis is false and that the two variables under investigation are related is not supported.Thus, the correct answer is D.
Learn more :
https://brainly.com/question/15409157?referrer=searchResults
Find the center and radius of the circle x2+y2=16
Answer:
The standard form of the equation of a circle is
(
x
−
a
)
2
+
(
y
−
b
)
2
=
r
2
where (a,b) are the coords of the centre and r , the radius.
x
2
+
y
2
=
16
is in this form
with a = b = 0 and r = 4
hence this circle has centre at the origin (0,0) and radius 4
The intercepts will therefore be (± 4,0) and (0, ± 4 )
In science class, Emily's 1-liter beaker contains 0.3 liter of water. Ali's beaker conatains 0.8 liter water, and Katies beaker contains 0.63 liter of water. who can pour all of her water into Emily's beaker without going over 1 liter.Ali or Katie?
Answer:
Step-by-step explanation:
KATIE
A basketball player makes 70% of the free throws he shoots. Suppose that he tries 15 free throws.
a. What is the probability that he will make more than 7 throws?
• enter your answer as a percent (56) or as a real-value (0.05)
. you enter your answer as a percent, you must use a-sign in your answer
• your answer must be accurate to the nearest whole percent.
b. How many baskets can the player expect to make it he takes 15 shots? .
. Your answers must be accurate to the nearest hundreth.
c. What is the standard deviation of the number of successful free throws out of 15 total?
Answer:
a.) .95
b.) The expected number of baskets is 10.50.
c.) 1.7748
Step-by-step explanation:
a.) This is a binomial distribution as there are two possibilities: makes a free throw or doesn't. This means that you can use the binomial function on a calculator to figure out the answer. Use the binomial CDF function on a calculator and the number of trials=15, probability of success=.7, lower bound=0, upper bound=7. Once you have evaluated the answer, .0500, it will need to be subtracted from1, as you want everything not included in this section. The answer to part a is thus 1-.0500=.95.
b.) The expected value is calculated by taking the total number of shots and multiplying it by the probability of making the shot: 15×.7=10.5 shots.
c.) The standard deviation of a binomial distribution can be calculated by the formula [tex]\sqrt{(sample size)(probability)(1-probability)}[/tex]. Plugging in the numbers you get [tex]\sqrt{(15)(.7)(.3)}[/tex]=1.7748.
A. The probability of more than 7 throws is 0.95,
B. The player expects to make it he takes 15 shots at 10.50,
C. The standard deviation of the number of successful free throws out of 15 total of 1.775.
What is binomial probability?The probability of exactly x successes on n repeated trials in an experiment with two possible outcomes, also known as a binomial experiment, is referred to as binomial probability.
The binomial probability is ⁿCₓpₓ(1 - p)ⁿ⁻ˣ if the probability of success on an individual trial is p.
In this case, the number of distinct combinations of x objects chosen from a set of n objects is shown by ⁿCₓ. A few course readings utilize the documentation (ⁿₓ) rather than ⁿCₓ.
Keep in mind that if p is the probability of a single trial's success, then (1p) is the probability of a single trial's failure.
Given the probability of free throws at 0.7
total free throws 15
Let x be the random variable
A. the probability that he will make more than 7 throws
p(x > 7)
ⁿCₓpₓ(1 - p)ⁿ⁻ˣ
where n = 15, x = 8
¹⁵C₈(0.7)⁸(0.3)⁷
0.94998 = 0.95
B: player expect to make it he takes 15 shots
E(x) = n x p(x)
E(x) = 15 × 0.7 = 10.50
C: The standard deviation
variance = n x p x q
variance = 15 x 0.7 x 0.3 = 3.15
SD = √(variance) = √(3.15)
SD = 1.77482 ≈ 1.775
Hence the probability that he will make more than 7 throws is 0.95,
the player expects to make it if he takes 15 shots is 10.50,
The standard deviation is 1.775.
Learn more about binomial probability;
https://brainly.com/question/29350029
#SPJ2
What is
2 1/8 - 1 7/8=?
Answer:
1/4
Step-by-step explanation:
2 1/8 - 1 7/8
Borrow 1 from the 2 in the form of 8/8
1 + 8/8+1/8 - 1 7/8
1 9/8 - 1 7/8
2/8
Simplify
1/4
Answer: 1/4
Step-by-step explanation:
To subtract mixed fractions, you need to first trun them into improper fractions.
[tex]2\frac{1}{8} =\frac{17}{8}[/tex]
[tex]1\frac{7}{8} =\frac{15}{8}[/tex]
[tex]\frac{17}{8} -\frac{15}{8} =\frac{2}{8} =\frac{1}{4}[/tex]
X^2-9x=0 does anyone know this?
Answer:
x = 9
x = 0
There are two answers to this questions that are above . Below is the steps.
Steps:
Step 1: Factor left side of equation.
x(x−9)=0
Step 2: Set factors equal to 0.
x=0 or x−9=0
x=0 or x=9
Answer:
x = 9
x = 0
Hope this helps.
Answer:
x=0 x= 9
Step-by-step explanation:
X^2-9x=0
Factor out an x
x(x-9) = 0
Using the zero product property
x =0 x-9=0
x=0 x= 9
The population of Wyoming is about ? Times the population of Colorado
An equation of an ellipse is given. x2 16 + y2 25 = 1 (a) Find the vertices, foci, and eccentricity of the ellipse. vertex (x, y) = 0,−5 (smaller y-value) vertex (x, y) = 0,5 (larger y-value) focus (x, y) = 0,−3 (smaller y-value) focus (x, y) = 0,3 (larger y-value) eccentricity 3 5 (b) Determine the length of the major axis.
Answer:
(a)
The vertices are at (0,-5) and (0,5).The coordinates of the foci are (0,-3) and (0,3).Eccentricity=3/5(b)Length of the major axis=10
Step-by-step explanation:
When the major axis of an ellipse is parallel to the y-axis.The standard form of the equation of an ellipse is given as:
[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]
Given the equation:
[tex]\dfrac{x^2}{16}+\dfrac{y^2}{25}=1[/tex]
(I)The coordinates of the vertices are [tex](0, \pm a)[/tex]
[tex]a^2=25\\a^2=5^2\\a=5[/tex]
Therefore, the vertices are at (0,-5) and (0,5).
(II)The coordinates of the foci are [tex](0, \pm c)$ where c^2=a^2-b^2[/tex]
[tex]c^2=a^2-b^2\\c^2=25-16\\c^2=9\\c=3[/tex]
The coordinates of the foci are (0,-3) and (0,3).
(III)Eccentricity
This is the ratio of the distance c between the center of the ellipse and each focus to the length of the semi major axis.
Simply put, Eccentricity =c/a
Eccentricity=3/5
(b)Length of the major axis
The length of the major axis=2a
=2(5)=10.
Academic tenure is when a teaching or research position is given to a professor indefinitely. By removing concerns about job security for scholars, offering tenure is thought to encourage freedom of thought, and leaves a tenured professor with the freedom to explore and hold a variety of views. One data set that was released by the Integrated Postsecondary Education Data System (IPEDS) in 2018 contained 1347 private schools, 743 of which had tenured faculty. Suppose that a prospective college student is considering whether to apply to private or public colleges. In addition to considerations about cost, graduation rates, etc., he wants to know about the quality of the education and decides to use tenure as a way of measuring this. He knows that the majority (more than 0.5) of public schools have avenues for professors to apply for tenure, and wants to test whether this is true for private schools as well. Which of the following is the correct null hypothesis in words?
A. The true proportion of private colleges in the U.S. that have tenure-track faculty is not equal to 0.5.
B. The true proportion of private colleges in the U.S. that have tenure-track faculty is 743/1347.
C. The proportion of private colleges in this sample that have tenure-track faculty is greater than 0.5 .
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
Write the correct alternative hypothesis in notation.
Answer:
The correct null hypothesis in words is:
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
[tex]H_0: \pi = 0.5[/tex]
Step-by-step explanation:
He wants to test the claim that the proportion of private schools that have avenues for professors to apply for tenure is significantly higher than 0.5, as happen with the public schools.
Then, the alternative hypothesis is:
[tex]H_a: \pi >0.5[/tex]
The null hypothesis represents the opposite claim, where the proportion is not significantly higher than 0.5. Then, the null hypothesis is expressed as:
[tex]H_0: \pi = 0.5[/tex]
The correct null hypothesis in words is:
D. The long-run proportion of private colleges in the US, that have tenure-track faculty is 0.5.
If Tina traveled 2,700 miles in 9 hours on her plane flight to her vacation destination, how fast was the plane traveling
Answer:
300miles/hour
Step-by-step explanation:
2,700 miles in 9 hours;
The rate would be the number of miles covered per hour which is ;
2700/ 9 = 300miles/hour
Can someone help Plz
Answer:
D = 67 inches
Step-by-step explanation:
The trend line is y = x+2 where x is the height
y = 65+2
y = 67
Answer: 67 inches tall
Step-by-step explanation:
y= x+2
y= 65+2
y= 67
A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.
Answer:
The answer is shown below
Step-by-step explanation:
Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a)
[tex]\frac{dy}{dt}\ \alpha\ y(1-y)[/tex]
[tex]\frac{dy}{dt}=ky(1-y)[/tex]
where k is the constant of proportionality, dy/dt = rate at which the rumor spreads
b)
[tex]\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\[/tex]
[tex]y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}[/tex]
At t = 2, y = 40% = 0.4
c) At y = 75% = 0.75
[tex]y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days[/tex]
