The 90% confidence interval for the population mean is (140.4, 147.6), derived from a sample with a mean of 144 and a standard deviation of 12.
Let's break down the steps used to calculate the 90% confidence interval for the population mean:
- Sample mean ([tex]\bar{x}[/tex]): 144
- Sample standard deviation (s): 12
- Sample size (n): 30
- Critical value at 90% confidence (z): 1.645
The formula for the confidence interval is:
[tex]\[ (\bar{x} - z \cdot \frac{s}{\sqrt{n}}, \ \bar{x} + z \cdot \frac{s}{\sqrt{n}}) \][/tex]
Calculate the standard error (SE):
SE = s / sqrt(n)
SE = 12 / sqrt(30)
SE ≈ 2.188
Calculate the margin of error (ME):
ME = z * SE
ME = 1.645 * 2.188
ME ≈ 3.594
Calculate the lower limit (L):
L = [tex]\bar{x}[/tex] - ME
L = 144 - 3.594
L ≈ 140.406
Calculate the upper limit (U):
U = [tex]\bar{x}[/tex] + ME
U = 144 + 3.594
U ≈ 147.594
So, the 90% confidence interval for the population mean is approximately (140.406, 147.594), which rounds to (140.4, 147.6) when considering the appropriate level of precision. Therefore, the correct answer is (D) (140.4, 147.6).
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Which is the correct simplified form of the expression x^1/2y^-1/3/x^1/4y^1/2
Answer:
(A)[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
Step-by-step explanation:
The given expression is:
[tex]\frac{x^{\frac{1}{2}}y^{\frac{-1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}[/tex]
Upon solving the given expression, we get
=[tex]{x^{\frac{1}{2}-\frac{1}{4}}{\cdot}}{y^{\frac{-1}{3}-\frac{1}{2}}}[/tex] (using the property of exponents and powers that if base is same then the powers gets added.)
=[tex]x^{\frac{1}{4}}{\cdot}y^{\frac{-5}{6}}[/tex]
=[tex]\frac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]
which is the required simplified form of the given equation.
Hence, option A is correct.
The _____ ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
The scale ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.
The ratio you're referring to is called the scale factor. The scale factor is the ratio of the length of one side of a polygon to the length of the corresponding side of a similar polygon. Let's denote this scale factor as ( k ).
To calculate the scale factor, you need to choose corresponding sides from the two similar polygons. Once you've chosen a pair of corresponding sides, divide the length of one side by the length of the corresponding side from the other polygon.
Let's say we have two similar polygons, Polygon A and Polygon B, and we want to find the scale factor between them. Let's denote the length of a side of Polygon A as [tex]\( L_A \)[/tex] and the length of the corresponding side of Polygon B as [tex]\( L_B \)[/tex]. Then, the scale factor, ( k ), is given by:
[tex]\[ k = \frac{L_A}{L_B} \][/tex]
This ratio will give you the scale factor between the two polygons.
What is the least common multiple of 50, 60, and 72?
Assembly Line A produces 45 units in the same time that it takes Assembly Line B to produce 37 units. If Line B produces 555 units, how many units does Line A produce during the same time?
Assembly Line A will produce 24975 units during the same time that Line B produces 555 units.
Explanation:Let's assume that the time it takes for Assembly Line A to produce 45 units is equal to the time it takes for Assembly Line B to produce 37 units. This means that the time it takes for Line A to produce 1 unit is equal to the time it takes for Line B to produce 1 unit.
Now, we can set up a proportion to find how many units Line A will produce during the same time that Line B produces 555 units:
45 units / 1 unit = x units / 555 units
Cross-multiplying, we get:
45 * 555 = x units * 1
x units = 24975 units
Therefore, Line A will produce 24975 units during the same time that Line B produces 555 units.
A total of 900 tickets were sold for a game for a total of $1,150. if adult tickets sold for $2.00 and children's tickets sold for $1.00, how many of each kind of ticket were sold?
what is the value of the function f(x)=1/4x-3 when x=12
6
1
0
-6
Find the square root of the fraction 64/100
If there are 365 days in a non-leap year, what number is christmas day?
There are 5,280 feet in 1 mile. If Riley ran 26,400 feet, how many miles did she run? [Type your answer as a number.]
Answer:
She ran 5 miles
Step-by-step explanation:
To solve this, we can easily use proportion.
The question state that there are 5,280 feet in a mile, We are ask to find the number of miles Rily run, if she ran 26,400 feet.
Using proportion;
Let x = the number of miles Rily can run
5,280 feet = 1 mile
26,400 feet = x
Cross-multiply
5280x = 26,400
To get the value of x, we will divide both-side of the equation by 5280
5280x/5280 = 26400/5280
(On the left-hand side of the equation, 5280 will cancel-out 5280 leaving us with x and on the right-hand side of the equation 26400 will divide 5280)
x = 26400 / 5280
x=5 mile
Therefore, If Rily ran 26400 feet, then she has ran 5 miles.
How to calculate standard deviation given mean and sample size?
Please help with these two questions thank you.
The volume of wax used in making a cylindrical candle is given by the formula v=nr2h what is the height of the candle in terms of the volume and radius?
How do I solve for x within a triangle?
Which set represents the range of the function shown?
{(-1,5),(2,8),(5,3),(13,-4)}
A- {-1,2,5,13}
B-{-4,3,5,8}
C- {(5,-1),(8,2),(3,5),(-4,13)}
D-{-4,-1,2,3,5,5,8,13}
Answer:
B. {-4,3,5,8}
Step-by-step explanation:
We are given,
The set representing the function is {(-1,5),(2,8),(5,3),(13,-4)}.
It is required to find the range set of the function.
Now, as we know,
In the ordered pair [tex](x,y)[/tex], the y co-ordinate 'y' represents the range values of a function.
So, we see that,
The range values of the given function are 5, 8, 3 and -4.
Thus, the set representing the range of the function is {-4,3,5,8}.
What is the image of (5,-1) under same translation?
The image of point (5, -1) under the same translation that maps point P to P' is (1, -8). This translation vector is obtained by subtracting the coordinates of P from P'.
To find the image of point (5, -1) under the same translation T that maps point P to P', we can calculate the vector that represents the translation from P to P' and then apply the same translation to point (5, -1).
The translation vector is given by:
Translation vector = P' - P = (-6, -4) - (-2, 3) = (-4, -7)
Now, to find the image of point (5, -1) under the same translation, we simply add this translation vector to (5, -1):
Image of (5, -1) = (5, -1) + (-4, -7) = (5 - 4, -1 - 7) = (1, -8)
So, the image of point (5, -1) under the translation T is (1, -8). Therefore, the correct answer is B. (1, -8).
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Multiply 5x2(2x2 + 13x − 5). 10x4 + 65x3 − 25x2 10x2 + 65x − 25 7x2 + 18x − 10 7x4 + 18x3 − 10x2
Answer:
[tex]10x^4+65x^3-25x^2[/tex]
Step-by-step explanation:
Multiply 5x^2(2x^2 + 13x − 5)
[tex]5x^2(2x^2 + 13x - 5)[/tex]
Multiply 5x^2 inside the parenthesis
[tex]5x^2 * 2x^2 = 10x^4[/tex]
[tex]5x^2 * 13x = 65x^3[/tex]
[tex]5x^2 * (-5) = -25x^2[/tex]
Collect all the terms together
[tex]10x^4+65x^3-25x^2[/tex]
How many true conditional statements may be written using the following statements?
n is a rational number.
n is an integer.
n is a whole number.
a.
2 conditional statements
c.
4 conditional statements
b.
3 conditional statements
d.
5 conditional statements
Suppose an investment of $10,000 doubles in value every 13 years. How much is the investment worth after 52 years? After 65 years?
A: $80,000; $100,000
B: $160,000; $320,000
C: $520,000; $650,000
Answer:
Step-by-step explanation:
The answer is actually B. $160,000; $320,000
The reason for this is because -
$10,000 is the constant, so let a= 10,000.
The investment doubles every 13 years, so let b=2.
Let x= the number of 13-year periods.
The value of a $10,000 investment doubling every 13 years will be $160,000 after 52 years and $320,000 after 65 years.
Explanation:To calculate the value of an investment that doubles every 13 years, you can determine the number of times the investment will double over a given period. In this case, after 52 years, the investment will have doubled 4 times (since 52 divided by 13 is 4), and after 65 years, it will have doubled 5 times (since 65 divided by 13 is 5).
The formula for the future value of an investment that doubles is: Future Value = Present Value × (2^number of doublings).
After 52 years, the investment's worth would be calculated as follows:
$10,000 × (2^4) = $10,000 × 16 = $160,000
After 65 years, the investment's worth would be:
$10,000 × (2^5) = $10,000 × 32 = $320,000
Therefore, the correct answers are $160,000 after 52 years and $320,000 after 65 years, which corresponds to choice B.
Leo is going to use a random number generator 400 times. Each time he uses it, he will get a 1 , 2 , 3 , 4 , or 5.What is the best prediction for the number of times that Leo will get an odd number?
Answer:
Close to 240 times but probably not exactly 240 times
Step-by-step explanation:
ruby is visiting San Francisco. From her hotel she walks 1 block west ans 4 blocks south to a coffee shop. Then she walks 5 blocks east and 6 blocks south to a museum. Where is the museum in relation to her hotel
Answer:
The museum is 4 blocks east and 10 blocks south from her hotel.
Step-by-step explanation:
It is given that ruby is visiting San Francisco. From her hotel she walks:
(a) 1 block west and 4 blocks south to a coffee shop.
(b) Then she walks 5 blocks east and 6 blocks south to a museum.
First she moves 1 block west and 4 blocks south and reached at point B. After that she walks 5 blocks east and 6 blocks south and reached at point D.
From the below figure it is noticed that point D is 4 blocks east and 10 blocks south from the origin because
[tex]South=4+6=10[/tex]
[tex]East=5-1=4[/tex]
Therefore the museum is 4 blocks east and 10 blocks south from her hotel.
solve for the variable r in this equation.
[tex] s=2 \pi rh[/tex]
Please and thanks! Also, it would help if you explained how you got your answer! (: ^-^
the equation 5x+4y=20 represents a linear function in two variables. Identify the slope, x-intercept and y-intercept of this linear function
180 is 10 % more than witch number ?
The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 10 + 15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
We are given a function H(t) that represents the height of a cannon ball after t seconds as:
[tex]H(t)=-16t^2+48t+12[/tex]
and a second cannon ball is represented by the function g(t) as:
[tex]g(t)=10+15.2t[/tex]
PART A:
t 0 1 2 3
H(t) 12 44 44 12
g(t) 15.2 25.2 40.4 55.6
Hence, between t= 2 seconds and t=3 seconds the ball will meet
such that H(t)=g(t)
Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.
and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.
Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.
and the time at which they meet is calculated by solving:
[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]
As t can't be negative.
Hence, we get:
t=2.109 seconds
PART B:
The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.
The graph of g(x) is the graph of f(x)=12x+6 compressed vertically by a factor of 13 .
Which equation describes the function g?
g(x)=12x+2
g(x)=4x+6
g(x)=4x+2
g(x)=36x+6
the temperature was -3 degrees last night. it is now -4 degrees . what was the change in the temperature
The sum of twice a number and four is fourteen. find the number.
2x +4 =14
2x =10
x =5
the number is 5
Which can be a next step in the construction of an angle with a side on line l that is congruent to ∠ABC?
To construct an angle with a side on line l that is congruent to ∠ABC, follow these steps: Draw line l, measure ∠ABC, draw a ray from line l with the same angle, label the intersection point as B, and segment AB is congruent to side AC.
To construct an angle with a side on line l that is congruent to ∠ABC, you can follow these steps:
Draw line l.
Use a protractor to measure ∠ABC.
Draw a ray from line l, starting at point A and making the same angle as ∠ABC.
Label the point where the ray intersects line l as B.
Now, segment AB is congruent to side AC of ∠ABC.
Yeet! I need some help! 16 points to whoever answers!
Find the value of m angle 3-m<1
Answer:
The value of [tex]m\angle 3-m\angle 1[/tex] = [tex]50^{\circ}[/tex]
Step-by-step explanation:
Vertical Angle theorem: It is about the angles that are opposite to each other.
Also, vertical angle are congruent that means vertical angles are equal.
In the given figure; [tex]m\angle 3[/tex] and [tex]70^{\circ}[/tex] are vertical angle
then, by vertical angle theorem, [tex]m\angle3 =70^{\circ}[/tex].
Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.
From the figure, [tex]70^{\circ}[/tex] , [tex]\angle 1[/tex] and [tex]m\angle 2 =90^{\circ}[/tex] forms a straight line.
then, by the definition of Supplementary angle;
[tex]70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}[/tex]
Substituting the value of [tex]m\angle 2 =90^{\circ}[/tex] in above equation:
[tex]70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}[/tex] or
[tex]160^{\circ}+m\angle 1=180^{\circ}[/tex]
Simplify:
[tex]m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}[/tex]
therefore, [tex]m\angle 1= 20^{\circ}[/tex] and [tex]m\angle 3=70^{\circ}[/tex],
the value of [tex]m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}[/tex].