Answer:
80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
Step-by-step explanation:
We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;
Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.
Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex] = 4.61
n = sample of people = 20
[tex]\mu[/tex] = true average number of hours of TV watched per week
Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.
So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;
P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80 {As the critical value of t at 19 degrees of
freedom are -1.33 & 1.33 with P = 10%}
P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80
P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80
80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]
= [8.28 hours, 11.02 hours]
Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].
If a graph of y=-9x+ 3 were changed to a graph of y=-9x + 1, how would the
y-intercept change?
Answer:
y-intercept decreased by 3-1= 2 points
Step-by-step explanation:
y=-9x+ 3 ⇒ y-intercept= 3
y=-9x + 1 ⇒ y-intercept= 1
y-intercept decreased by 3-1= 2 points = the line shifted down by 2 points
Answer:
Hello!
Answer: y-intercept decreased by 2 points because 3-1=2
I hope I was of help. If not, please let me know! Thanks!
Step-by-step explanation:
Calculate the surface area of the egg (in μm2). The formula for calculating the surface area (SA) of a sphere is given below. SA = 4Ïr2. Use 3.14 as the value for Ï.
Answer:
[tex]31400\mu m^2[/tex]
Step-by-step explanation:
We are given that
Diameter of egg,d=[tex]100\mu m[/tex]
We have to find the surface area of egg in [tex]\mu m^2[/tex].
Radius of egg,r=[tex]\frac{d}{2}=\frac{100}{2}=50\mu m[/tex]
Surface area of sphere=[tex]4\pi r^2[/tex]
Where [tex]\pi=3.14[/tex]
Using the formula
Surface area of egg=[tex]4\times 3.14(50)^2[/tex]
Surface area of egg=[tex]31400\mu m^2[/tex]
Hence, the surface area of the egg=[tex]31400\mu m^2[/tex]
Ravi's age is six times that of Gaurav's. After 8 years Ravi will be twice as old as Gaurav. What are their present ages?
Answer:
10 and 2
Step-by-step explanation
Nitesh is currently 10 and Ravi is currently 2
(2 times 5 is 10)
in 2 years Nitesh will be 12 and Ravi will be 4
(4 times 3 is 12)
Find the value of x in the figure below
88°
Step-by-step explanation:
sum of angle=720
95+120+120+172+125+x=720
632+x=720
×=720-632
x=88
Answer:
[tex] \boxed{x \degree = 88 \degree} [/tex]
Step-by-step explanation:
Sum of the interior angles of a hexagon is 720°
[tex] = > x \degree + 172 \degree + 120 \degree + 95 \degree + 120 \degree + 125 \degree = 720 \degree \\ \\ = > x \degree + 172 \degree + 240 \degree + 220 \degree = 720 \degree \\ \\ = > x \degree + 172 \degree + 460 \degree = 720 \degree \\ \\ = > x \degree + 632 \degree = 720 \degree \\ \\ = > x \degree = 720 \degree - 632 \degree \\ \\ = > x \degree = 88 \degree[/tex]
Do you think a sequence of translations across the x- or
y-axis and/or reflections on a figure could result in the
same image as a 90-degree clockwise rotation? Explain
why or why not.
I think just two reflections would do it.
First we reflect around y = -x, the 45 degree line through the origin and the second and fourth quadrant.
Then we reflect through the y axis, x=0.
The composition of the two reflections is equivalent to a 90 degree clockwise rotation.
Answer: No, it is not possible to get the same image as a 90-degree clockwise rotation using only translations and/or reflections. In the rotation, the x- and y-coordinates are switched. There is no way to reverse the order of the coordinates using only reflections or translations.
Step-by-step explanation:
ITS CORRECT. EDGE 2020
4 ounces for every 16 ounces. Rate or ratio and in simplest form
4 for 16 would be written as 4/16.
Dividing both numbers by 4 it is simplified to 1/4
4 ounces for every 16 ounces can be written as:
[tex]\displaystyle \frac{4}{16} =\frac{1}{4}[/tex]
As a ratio, it can be expressed as:
[tex]1:4[/tex]
To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.
Answer:
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
Step-by-step explanation:
We need to take in count that we are conducting a regression model with just one dependent variable and 3 independent variables
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
What do you know to be true about the values p and q
Answer:
B
Step-by-step explanation:
The sum of all angles in a triangle must equal 180 degrees. Knowing this, you can find the values of p and q.
p
80 + 20 + p = 180
100 + p = 180
100 - 100 + p = 180 - 100
p = 80
q
55 + 45 + q = 180
100 + q = 180
100 - 100 + q = 180 - 100
q = 80
Conclusion
That means that p & q are equal to one another.
I hope this helps! Have a great day!
The thing that's true about the values p and q is that p = q.
The total sum of the angles in a triangle is 180°.
From the first triangle, the value of p will be:
80° + 20° + p = 180°
100° + p = 180°
p = 180° - 100°
p = 80°
From the second triangle, the value of q will be:
55° + 45° + q = 180°
100° + q = 180°
q = 180° - 100°
q = 80°
Therefore, p = q.
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Given the following, determine the set (A'U B')∩C.
U = {x |x ∈ N and x < 10}
A = {x | x∈ N and x is odd and x < 10)
B = {x|x ∈ N and x is even and x < 10}
C = {x|∈E N and x < 8)
Answer:
n +10 =20
Step-by-step explanation:
answer =20 . thank God
If f(x)=x³-2x², which expression equivalent to f(i)?
Answer:
f(x) = x³ - 2x²
=>
f(i) = i³- 2i²
Hope this helps!
:)
2- = - 6 – 4.0
Solve for x:
5. There are 400 students in the senior class at Oak Creek High School. All 2 points
of these students took the SAT. The distribution of their SAT scores is
approximately normal. The number of students who scored within 2
standard deviations of the mean is approximately *
-3
-2
0
1
2.
3
Answer:
The number of students who scored within 2 standard deviations of the mean is 380.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
The number of students who scored within 2 standard deviations of the mean is approximately
By the Empirical Rule, 95% of the students scored within 2 standard deviations of the mean
Out of 400
0.95*400 = 380
The number of students who scored within 2 standard deviations of the mean is 380.
Answer: 380
Step-by-step explanation: 95% of 400 is 380
If f(x)=7+4c and g(x) = 1/2x what is the value of (f/g)(5)
Answer: 270
Step-by-step explanation:
The notation [tex](\frac{f}{g})(5)[/tex] means to divide [tex]\frac{f(5)}{g(5)}[/tex]. Now that we know we have to divide, we can plug them into this equation.
[tex]\frac{7+4(5)}{\frac{1}{2(5)} }=\frac{27}{\frac{1}{10} }[/tex]. We know that dividing by a fraction means to multiply by its reciprocal, so we'll do that.
[tex]27*10=270[/tex]
what is the slope from 1 to 5.3 seconds?
Answer:
3/2
Step-by-step explanation:
The graph rises 3 feet for each 2 seconds to the right. The slope is ...
rise/run = (3 ft)/(2 s) = (3/2) ft/s
The numerical value of the slope is 3/2 or 1.5. The associated units are feet per second.
A four-year study of various brands of bottled water found that 25% of bottled water is just tap water packaged in a bottle. Consider a sample of sevenseven bottled-water brands, and let x equal the number of these brands that use tap water. Complete parts a through d.
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Answer:
Answers below
Step-by-step explanation:
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
which rule represents the translation from the pre-image ABCD, to the image, a’b’c’d’
Answer:
Pre-image ABCD has been shifted 2 units right and 1 unit upwards.
Step-by-step explanation:
Coordinates of the points A,B,C and D of the pre-image ABCD,
A(-4, 4), B(-1, 4), C(-5, 1), D(-2,1)
Coordinates of the points A', B', C' and D' of the image A'B'C'D'.
A'(-2, 5), B'(1, 5), C'(-3, 2), D'(0, 2)
Now we choose points A from the pre-image and A' from the image,
A(-4, 4) → A'(-2, 5)
Rule for the translation will be,
A(-4, 4) → A'(-4+2, 4+1)
Or A(x, y) → A'(x+2, y+1)
Therefore, pre-image ABCD has been shifted 2 units right and 1 unit upwards to form image A'B'C'D'.
Answer: It's D
Step-by-step explanation:
the last one I just took the quiz
A battery with 20% percent of its full capacity is connected to a charger. Every minute that passes, an additional 5% percent of its capacity is charged. How do you graph this
Answer:
The relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
The graph is attached.
Step-by-step explanation:
We will graph the charged capacity of the battery in function of time.
The rate of charge is constant, so we can conclude the relation is linear.
At time t=0, the battery capacity is at 0.2 (or 20%).
Every minute that passes, an additional 5% percent of its capacity is charged. So we can say that at t=1, the battery capacity is 0.2+0.05=0.25 (or 25%).
We can calculate the slope of the linear function as:
[tex]m=\dfrac{\Delta Y}{\Delta t}=\dfrac{0.05}{1}=0.05[/tex]
Then, the relation between battery capacity and time is:
[tex]Y=0.05t+0.2[/tex]
What are the roots of x in -10x^2 + 12x − 9 = 0
Answer:
No roots
Step-by-step explanation:
the discriminant Δ = 12²-4×(-10)×(-9) = -216
since ∆ is negative then the equation -10x^2 + 12x − 9 = 0 has no solution .
Given that y = 1.5 at x = -2. Find the function y = f(x) such that
dy/dx=√(4y+3)/x²
Answer:
[tex]y=\frac{(-\frac{4}{x}+1)^2-3 }{4}[/tex]
Step-by-step explanation:
We are given the following information. y have the point [tex](-2,\frac{3}{2} )[/tex] and [tex]\frac{dy}{dx} =\frac{\sqrt{4y+3} }{x^2}[/tex]
First, we need to separate the variables to their respective sides
[tex]\frac{1}{\sqrt{4y+3} } dy=\frac{1}{x^2} dx[/tex]
Now, we need to integrate each side
[tex]\int \frac{1}{\sqrt{4y+3} } dy=\int\frac{1}{x^2} dx[/tex]
But first, let us rewrite these functions
[tex]\int (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Before we can integrate, we need to have the hook for the first function. When we integrate [tex](4y+3)^{-\frac{1}{2} }[/tex], we must have a lone 4 within the integral as well.
[tex]\frac{1}{4} \int4 (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]
Now we can integrate each side to get
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + c[/tex]
Now is the best time to use the given point in order to find the value of c.
[tex]\frac{1}{4} \sqrt{4(\frac{3}{2}) +3} =-\frac{1}{-2} + c\\\\\frac{1}{4}\sqrt{6+3} =\frac{1}{2} +c \\\\\frac{3}{4}=\frac{1}{2} +c\\ \\c=\frac{1}{4}[/tex]
Now we can plug in our value for c and then solve for y
[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + \frac{1}{4} \\\\\sqrt{4y+3}=-\frac{4}{x} +1\\ \\4y+3=(-\frac{4}{x} +1)^2\\\\4y=(-\frac{4}{x} +1)^2-3\\\\y=\frac{(-\frac{4}{x} +1)^2-3}{4}[/tex]
If f(x)=4arctan(7x), find f'(x). Find f'(4).
f'(x) = (4 arctan(7x))'
f'(x) = 4 (arctan(7x))'
By the chain rule,
f'(x) = 4/(1 + (7x)^2) * (7x)'
f'(x) = 28/(1 + 49x^2)
and hence
f'(4) = 28/(1 + 49*16) = 28/785
In case you're not sure about the derivative of arctan: If y = arctan(x), then x = tan(y). Differentiating both sides with respect to x gives
1 = sec^2y y' = (1 + tan^2y) y' = (1 + x^2) y'
==> y' = 1/(1 + x^2)
Pythagorean theorem please help
Answer:
4√73
Step-by-step explanation:
x^2= 12^2 + 32^2
x^2= 144+ 1024
x^2=1168
x= 4√73
A circular garden has a diameter of 12 feet. About how much trim is needed to surround the garden by placing trim on the garden's circumference? 38 ft or 48 ft or 144 ft or 432 ft
Answer:
About 38 feet
Step-by-step explanation:
The formula for a circle's circumference is 2 times pi times r, which is the radius.
Since the diameter is 12, the radius is half the diameter, so the radius is 6.
2 times pi times 6 is about 37.7 feet, or 38 feet.
Hope this helped.
The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]
[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]
A prism is filled with 3 layers of cubes. Each layer has 25 cubes. The volume of each cube is 1 cubic inch. What is the volume of the prism?
Answer:
The volume of the prism is 75 cubic inches
Step-by-step explanation:
The volume of the prism is the amount of space contained on the interior of the prism.
Now we have that this entire space is filled with cubes of defined volumes. Therefore, to get the volume of the prism, we can simply get the total volume occupied by all the cubes. This should give us our answer.
From the information we are given, we know that the there are 3 layers of cubes each containing 25 cubes.
This gives the total number of cubes to be 3 X 25 = 75 cubes in total
We also know that the volume of 1 cube is 1 cubic inch.
Hence the volume of 75 cubes will be 75 X 1 cubic inch = 75 cubic inches.
Help Me PLEASE!!!
A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?
Answer:
P = 0.5207
Step-by-step explanation:
First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.
Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).
So, the probability that just the first card is a diamond or an ace is calculated as:
[tex]P_1=\frac{16}{52}*\frac{36}{52}=0.2130[/tex]
At the same way, the probability that just the second card is a diamond or an ace is:
[tex]P_2=\frac{36}{52}*\frac{16}{52}=0.2130[/tex]
Finally, the probability that both cards are diamonds or aces is:
[tex]P_3=\frac{16}{52}*\frac{16}{52}=0.0947[/tex]
Therefore, the probability that at least one of the cards is a diamond or an ace is:
[tex]P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207[/tex]
A real estate purveyor purchases a 60{,}00060,00060, comma, 000 square foot \left(\text{ft}^2\right)(ft 2 )(, start text, f, t, end text, squared, )warehouse and decides to turn it into a storage facility. The warehouse's width is exactly \dfrac 2 3 3 2 start fraction, 2, divided by, 3, end fraction of its length. What is the warehouse's width? Round your answer to the nearest foot.
Answer:
200 feet
Step-by-step explanation:
Area of the warehouse [tex]=60,000$ ft^2[/tex]
Let the length of the warehouse=l
The warehouse's width is exactly [tex]\dfrac23[/tex] of its length
Therefore: Width of the warehouse[tex]=\dfrac23l[/tex]
Area =Length X Width
Therefore:
[tex]\dfrac23l*l=60000\\$Cross multiply\\2l^2=60000*3\\2l^2=180000\\$Divide both sides by 2\\2l^2 \div 2=180000 \div 2\\l^2=90000\\l^2=300^2\\$Length, l=300 feet\\Recall: Width =\dfrac23l\\$Therefore, Width of the warehouse=\dfrac23*300=200$ feet[/tex]
Change the fraction1/5 to a percent
Answer:
Step-by-step explanation:
which statement about numbers is true
Answer:
what are the answers fir this question
Answer:
Answer options are:
a. All integers are natural numbers.
b. All rational numbers are integers.
c. All natural numbers are whole numbers.
d. All rational numbers are natural numbers.
Step-by-step explanation:
Answer is C
In 2018, the number of students at The Villages High School was 975 and is increasing at a rate of 2.5% per year. Write and use an exponential growth function to project the populating in 2025. Round to the nearest whole number. Help plzzz
Answer:
[tex]A(t)=975(1.025)^t[/tex]
In 2025,the number of students at the villages high school=1159
Step-by-step explanation:
We are given that in 2018
Number of students at the villages high school=975
Increasing rate,r=2.5%=0.025
We have to write and use of exponential growth function to project the populating in 2025.
[tex]A_0=975,t=0[/tex]
According to question
Number of students at the villages high School is given by
[tex]A(t)=A_0(1+r)^t[/tex]
Substitute the values
[tex]A(t)=975(1+0.025)^t=975(1.025)^t[/tex]
t=7
Substitute the value
Then, the number of students at the villages high school in 2025
[tex]A(7)=975(1.025)^7=1158.96\approx 1159[/tex]
Answer:
1,159 students
Step-by-step explanation:
the exponential growth rate formula:
A = P ( 1 + r)ⁿ
A = amount after growth = ??P = current/original amount = 975 studentsr = yearly growth rate = 2.5% or 0.025n = number of years = 2025 - 2018 = 7Pop. 2025 = 975 (1 + 0.025)⁷
Pop. 2025 = 975 x 1.025⁷ = 1,158.97 ≈ 1,159 students
(04.03 MC)
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
A coordinate plane with quadrilateral ABCD at A 0 comma 3, B 2 comma 4, C 4 comma 0, and D 2 comma negative 1. Angles A and C are right angles, the length of segment AB is 2 and 24 hundredths units, and the length of diagonal BD is 5 units.
8.96
10.48
13.42
20.42
The units of tile will he need to surround his pool is 13.42
The given parameters are:
[tex]AB =2.24[/tex]
[tex]BD =5[/tex]
Start by calculating the distance BC using the following Pythagoras theorem
[tex]BD^2 = AB^2 + BC^2[/tex]
So, we have:
[tex]5^2 = 2.24^2 + BC^2[/tex]
[tex]25 = 5 + BC^2[/tex]
Collect like terms
[tex]BC^2 = 25 - 5[/tex]
[tex]BC^2 = 20[/tex]
Take the square roots of both sides
[tex]BC = 4.47[/tex]
The unit of tiles is then calculated using the following perimeter formula
[tex]Tiles = 2 \times (AB + BC)[/tex]
So, we have:
[tex]Tiles = 2 \times (2.24 + 4.47)[/tex]
[tex]Tiles = 13.42[/tex]
Hence, the units of tile will he need to surround his pool is 13.42
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