Answer:
n=438
Step-by-step explanation:
-Given the sample proportion [tex]\hat p=0.24[/tex] and the confidence level is 95%.
-The sample size can be calculated using the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
#Substitute parameters in the formula and make n the subject of the formula;
[tex]ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=z_{0.025}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\n=(\frac{z_{0.025}}{ME})^2\hat p(1-\hat p)\\\\\\=(\frac{1.96}{0.04})^2\times 0.24\times 0.76\\\\=437.94\approx 438[/tex]
Hence, the desired sample size is n=438
PLEASE HELP
55 50 54 57 50 55 53 52 55
What is the median length of the data?
50 mm
54 mm
55 mm
57 mm
Answer:
54mm
Step-by-step explanation:
50, 50, 52,53, 54, 55, 55, 55, 57
Which expression is equivalent to StartFraction b Superscript negative 2 Baseline Over a b Superscript negative 3 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.
Given:
The given expression is [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Let us assume that [tex]a \neq 0, b \neq 0[/tex]
We need to determine an expression that is equivalent to the expression [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Equivalent expression:
The equivalent expression can be determined by solving the given expression.
Hence, applying the exponent rule, [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]
Thus, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b^{-2-(-3)}}{a}[/tex]
Subtracting the numbers, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b}{a}[/tex]
Thus, the equivalent expression is [tex]\frac{b}{a}[/tex]
Hence, Option D is the correct answer.
Answer:
d
Step-by-step explanation:
3. Suppose m = 2 + 6i, and |m+n|=3√10, where n is a complex number.
a. What is the minimum value of the modulus of n?
b. Provide one example of the complex number, n.
Answer:
Answer:
Step-by-step explanation:
Suppose m = 2 + 6i, and |m+n|=3√10,
The modulus sign means m+n can either be positive or negative as shown.
If it is positive:.2+6i+n = 3√10
n = 3√10-(2+6i)
n = 3√10-2-18√10i
n = (-2+3√10)+√10i
b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.
Ms. Lopez draws two cylinders on the whiteboard. The first cylinder has a diameter of 6 inches and a height of 14 inches. The second cylinder has a diameter of 3 inches.
If the second cylinder has the same ratio of diameter to height, what is its height?
Answer:
7 inches
Step-by-step explanation:
Height : Diameter
14 : 6
H : 3
H/14 = 3/6
H = 14 × 3/6
H = 7
Answer:
7 inches
Step-by-step explanation:
You purchased a boat for $19,000 and can expect the boat to depreciate at an annual rate of 7.3%. What will the value of your car be 4 years after purchasing it
Answer:
$14,030.48
Step-by-step explanation:
We can use the following formula to solve:
[tex]A=P(1-r)^t[/tex]
P = principal value
r = rate (decimal)
t = time (years)
First, lets change 7.3% into a decimal:
7.3% -> [tex]\frac{7.3}{100}[/tex] -> 0.073
Next, plug in the values:
[tex]A=19,000(1-0.073)^4[/tex]
[tex]A=14,030.48[/tex]
The value will be $14,030.48
Determine which of the following graphs does not represent a function
(Help me ASAP please)
Answer:
C
Step-by-step explanation:
In order to be a function, all of the graphs need to pass the vertical line test
Vertical line test- Only one point per vertical line, if there are more than one, it is not a function
C is the only one that has more than one point at a vertical line
The answer is c. If there are 2 points in a vertical line, it is not a function.
What Is the lateral area of the triangular pyramid?
Answer: 169.6
Step-by-step explanation:
The lateral area of a triangular pyramid is calculated by finding the area of each of the pyramid's three triangular faces and adding them together. This process is simplified if the pyramid is equilateral.
Explanation:To calculate the lateral area of a triangular pyramid, you start by finding the area of each of the three triangular faces (the base is not included). If the pyramid has equal sides (an equilateral triangular pyramid), the process is simplified. The area of a single triangle face is found using the formula 0.5*base*height. Then simply multiply this by 3 since there are three faces. If the pyramid doesn't have equal sides, you will need to calculate the area of each face separately and then add them together to find the total lateral area.
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PLEASE HELP!!!Hannah conducts an investigation to determine if adding fertilizer to the soil helps tomato plants grow taller. She puts 20 tomato plants in individual pots and adds an equal amount of soil to each pot. All 20 plants are the same height at the beginning of the investigation. She adds the same amount of fertilizer to the soil of 10 pots. Hannah measures the height of each plant once a day for 15 days. The presence of fertilizer in the soil is the . The height of the tomato plants is the . The pots without fertilizer are the .
Answer:
1. independent variable
2. dependent variable
3. control group
Step-by-step explanation:
Independent variables are the factors in the experiment that are being modified to discover some sort of result.
Dependent variables are those that change because of the independent variable; they're also the ones that are measured in the experiment.
The control group is a group that undergoes the same exact procedure as the experimental group(s) do, but without the independent variable; it is to make sure that the different results aren't due to environmental factors.
Here, because Hannah is changing the amount of fertilizer in the plants (none or a specific amount), the presence of fertilizer is the independent variable. Since the heights of the plants will likely change due to the presence of fertilizer, height is the dependent variable. And, finally, the pots without fertilizer undergo the same procedure but without the independent variable, or the fertilizer, so it's the control group.
Hope this helps!
Answer:
The presence of fertilizer in the soil is the independent variable
The height of the tomato plants is the dependent variable
The pots without fertilizer form the control group
Step-by-step explanation:
She has divided the pots into 2 groups of 10 each:
1) experimental group
2) control group
She can decide the amount of fertiliser so that's an independent variable
What's she's observing are the heights which she can't control so heights is the dependent variable
How many children answered
any adults?
Answer:
Step-by-step explanation:
Solve the system of equations
x + 3y = 5
-x + 6y = 4
A) x = 1, y = 2
B) x = 2, y = 1
C) x = 1, y = 1
D) x = 0, y = 2
Answer:
B) x = 2, y = 1
Step-by-step explanation:
Add the two equations to eliminate the x-variable.
(x +3y) +(-x +6y) = (5) +(4)
9y = 9 . . . . . . .simplify
y = 1 . . . . . . . . divide by 9
You can substitute this value into either equation to find x.
x + 3(1) = 5
x = 2 . . . . . . . . subtract 3
The solution is (x, y) = (2, 1).
Answer:
B) x=2, y=1
Step-by-step explanation:
x+3y=5
-x+6y=4
solve the equation
x=5-3y
-x+6y=4
substitute the value of x into an equation
-1(5-3y)+6y=4
multiply numbers in parenthesis by -1
-5-3y+6y=4
put -5 as positive and add 5 to 4 and put -3y as positive and add to 6y.
9y=9
divide both sides by 9
y=1
substitute the value of y into an equation
x=5-3•1
multiply 3 to 1
x= 5-3
subtract 5 to 3
x=2
------------
x=2
y=1
------------
I need help with this
Answer:
Step-by-step explanation:
Fill in the blanks:
a. range
b. median
c. mode
d. mean
1. mean: 5+3+2+6+5+2+5= 15+4+6+3= 28/7= 4
median: 2,2,3,5,5,5,6: 5
mode: 5
range: 6-2= 4
2. 24+12+10+15+10+22+12= 105/7= 15 mean
10,10,12,12,15,22,24: 12 is the median
mode: 10, 12
range: 24-10= 14
3. 14+9+20+5+17+13= 78/6= 13 is the mean
5,9,13,14,17,20: 13+14= 27/2= 13.5 median
no mode
20-5= 15 the range
4. 21+15+16+25+13+18= 108/6= 18 is the mean
median: 13,15,16,18,21,25: 16+18= 34/2= 17
no mode
range: 25-13= 12
5. 10+12+17+18+20+25+31= 133/7= 19 mean
median: 18
mode: none
range: 31-10=21
6. 40+43+46+48+52+53= 282/6= 47
median: 46+48= 94/2 = 47
mode: none
range: 53-40= 13
7. 8+9+10+15+28= 70/5= 14 mean
median: 10
mode: none
range: 28-8= 20
8. 22+32+33+58+85= 230/5= 46 mean
median: 33
mode: none
range: 85-22= 63
9. 17+18+20+24+30+35= 144/6= 24 mean
median: 24+20= 44/2= 22
mode: none
range: 35-17= 18
10. 116+120+125+125+130+140= 756/6=126: mean
median: 125+125= 250/2= 125
mode: 125
range: 140-116= 24
In the diagram, point C represents the center of the sphere. Diego says that the part of the sphere labeled D is the radius. Gregoire says that the part of the sphere labeled D is the diameter of the sphere.
A sphere. C is the center and D is the diameter.
Who is correct and why?
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Gregoire is correct; the diameter is a chord that is from the center to the surface of the sphere.
Diego is correct; the radius is a chord that passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
HELPPPP ASAPPP PLEASEEEEEE!!!!!!
Answer:
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Step-by-step explanation:
A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.
The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.
A diameter is twice of a radius, so that:
Radius = [tex]\frac{Diameter}{2}[/tex]
⇒ Diameter = 2 × Radius
Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.
Answer:
a
Step-by-step explanation:
The area of a playground is 168 yd2. The width of the playground is 2 yd longer than its length. Find the length and width of the playground. Then, enter the sum of the length and width in the provided grid.
[ ] [ ] [2] [6]
/ ОО
. ООООO
0 ОООО
1 ОООО
2 ОООО
3 OOOO
4 ОООО
5 ОООО
6 OOOO
7 OOOO
8 OOOO
9 OOOO
Answer:
Length = 12yards
Width = 14yards
Sum = 26yards
Step-by-step explanation:
Let assume the play ground is rectangular in form.
Area of a rectangle = length × width
Given area of the playground = 168yd²
If the width of the playground is 2yd longer than its length, then:
W = L+2
Substituting W = L+2 into the formula above we have:
A = L × (L+2)
A = L²+2L
168 = L²+2L
L²+2L-168 = 0
L²+14L-12L-168 = 0
L(L+14)-12(L+14) = 0
(L-12)(L+14) = 0
L-12 = 0 and L+14 =0
L = 12 and -14
Taking the positive length, L = 12yards
If Length = 12yards
W = L+2
W = 12+2
Width = 14yards
Sum of the length and width will be:
L+W= 12+14
= 26yards
Answer:
The length of playground is 12 yd
The width of playground is 14 yd
The sum of the length and width of playground is 26 yd
Step-by-step explanation:
The area, A of the playground is given as 168 yd²
The formula for the area of the playground is given as follows;
Area, A of playground = Length, L × Width, W
The Width = length + 2 yd or W = L + 2
Therefore, A = L × (L + 2)
A = L² + 2·L
Where we have A = 168 yd², we have the area equation presented as follows
168 = L² + 2·L or
L² + 2·L - 168 = 0
Factorizing the above equation gives
L = 12 or L = -14 we note that the appropriate solution is L = 12 yd
Therefore W = L + 2 = 12 + 2 = 14 yd
The length of playground = 12 yd
The width of playground = 14 yd
The sum of the length and width of playground = 12 + 14 = 26 yd.
(18,15) and (36,30) whats the slope?
Answer:
5/6
Step-by-step explanation:
Rise over run
y2-y1 / x2-x1
30-15 / 36-18
Hope this helps!
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DO NOT SPAM
DO NOT ADD USELESS ANSWERS TO GET THE POINTS
Question is in the screenshot below
Answer:
I think it would be 4/5 of a chance?
Step-by-step explanation:
Answer:
4/5
Step-by-step explanation:
Lincoln wants to mix 3/8 of a liter of red paint with 7/8 of a liter of blue paint to make purple paint. How many liters of purple paint will Lincoln make by mixing the two colors?
Answer: 1 1/4
Step-by-step explanation:
Solving the fraction parts
3/8 + 7/8 = 10/8
Reducing the fraction part, 10/8
10/8= 5/4
Simplifying the fraction part, 5/4
5/4= 1 1/4
Answer:
10/8
Step-by-step explanation:
You add 7/8 + 3/8 and that equals 10/8
I hope that's helpful
what is the product of (x+9)(x-9)
Answer:
x^2 - 81
Step-by-step explanation:
There is a formula called the difference of squares, which is
(a+b)(a-b) = a^2 - b^2
Answer: 9x²-81x
Step-by-step explanation:
1. Reorder the terms like this: (9x)• (x-9)
2. Remove unnecessary Parentheses like this: 9x•(x-9)
3. Distribute 9x through the Parentheses like this:
9x would become 9x² (because I combined 9x and 9x which become 9x²)
(x-9) would become -81x (so if you need further explanation I took the (x-9) and made it -9x then multiplied it by the 9x because of distributive property.)
The solution: 9x²-81x
Convert the decimal expansion of 0.152 into a rational number (fraction) in the simplest form
Answer:
The answer to your question is 77/500
Step-by-step explanation:
Data
decimal number = 0.154
fraction number = ?
Process
To convert a decimal number into a fraction, express the decimal number without the zero and the decimal point (this number will be the numerator) and write as a denominator a number one plus as many zeros after this number as numbers there are after the decimal point of the numerator.
Example
0.154 has three number after the decimal point then we write 1000
154/1000 =
Simplify
77/500
Given ABC = EDC find m
Answer: m<D = 80º
Step-by-step explanation:
Since we know triangle ABC is congruent to triangle EDC, the angle 60º can be know for angle ACB. Triangles have a interior total of 180, so 40+60 is 100. Subtract 100 from 180 to get your angle of B. Since the triangles are similar we know that B=D so D=80º
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
Set 1: 82, 80, 90
Set 2: 82, 80, 60, 90
The MAD of set 1 is 6 less than the MAD of set 2.
The MAD of set 1 is 5 less than the MAD of set 2.
The MAD of set 1 is 5 more than the MAD of set 2.
The MAD of set 1 is 6 more than the MAD of set 2.
Answer:
The answer is The MAD of set 1 is 5 less than the MAD of set 2.
Step-by-step explanation:
Santiago buys T-shirts for $6 each and marks up the price by 45%. How much profit does Santiago make from each T-shirt sold?
Answer:
Santiago earns 8.7 $ from each sold shirt
Step-by-step explanation:
1). 45 % of 6 is = 6 * 0.45 = 2.7 $
2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer
PLEASE HELP ME IF YOU CAN!
Answer:
y = 5[tex]e^{tan(x)}[/tex]
Step-by-step explanation:
work in picture below
Find the indicated limit, if it exists.
Answer:
limit is 2.
Step-by-step explanation:
f(x) = 10x + 2 for x< 0 ,
f(x) = |2 - x| for x>=0
get x close to 0
lim 10x + 2 x-->0- = 2
lim |2 - x| x-->0+ = 2
in a class of 30 students,13 of them are boys what parcentage of the class are girl give your aswer to 1 decimal place
Answer:
56.7% to one decimal place
Step-by-step explanation:
30 students
13 are boys
30-13=17
17 are girls
As a decimal 0.5667
As a percentage 56.67%
56.7% to one decimal place
The suns diameter is about 860,000 miles. It's diameter is about 8000 miles. Estimate how many times larger the sun's diameter is than earth's diameter
Answer:
The Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
Step-by-step explanation:
We are given the following in the question:
Sun's diameter = 860,000 miles
Earth's diameter = 8000 miles
Comparison of Sun's and Earth's diameter:
[tex]\dfrac{\text{Sun's Diameter}}{\text{Earth's Diameter}}\\\\=\dfrac{860000}{8000}\\\\=\dfrac{8.6\times 10^{5}}{8\times 10^3}\\\\=1.075\times 10^2[/tex]
Thus, the Sun's diameter is [tex]1.075\times 10^2[/tex] times the Earth's diameter.
A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?
The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28
Explanation:
School students = 40
Total people = 130
Total contestant spot = 9
Probability of 3 contestant from school = ?
The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃
The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆
The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆
The total number of possible 9 contestants from the audience = ¹³⁰C₉
Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]
Solving the equation further we get:
Probability of the group of contestants having 3 students = 0.28
Find the value of x
6
5
10
Answer:
10
Step-by-step explanation:
You can use process of elimination for this question
Since one of the chord is drawn in and part on the radius is connected to it, that "part" radius bisects the chord
Therefore, the chord is 16 units long
Then the diameter must be even longer
The only option that works for the radius is 10 as the diameter would be 20
If the radius was 5, the diameter would be 10 which is less than the chord
If the radius was 6, the diameter would be 12 which is less than the chord
Jim has to choose between two gym membership plans. Plan A has a $50 initial fee and then it costs $10 per visit. Plan b has a initial $25 membership fee and then it will cost her $15 per visit
If we are looking for when they would be the same at a given time:
First, we need to set them to each other:
50 + 10x = 25 + 15x
Move them around and then get this:
25 = 5x
Divide by 5 from both sides
5 = x
fractions that are equivent to 4/12
Answer:
1/3 2/6
Step-by-step explanation:
Answer:
2/6 and 1/3
Step-by-step explanation:
For a game show, Jared has to choose 1 of 8 boxes to win a prize. One of the boxes has a big prize, 3 boxes have a medium prize, 3 boxes have smaller prizes, and 1 box is empty. How confident should Jared be that whatever box he chooses, he will win a prize?
Answer:
He should be very confident
Step-by-step explanation:
He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing
The probability that the box selected will win the prize is A = 7/8 = 87.5 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the box selected will win the prize be A
Now , the total number of boxes = 8
The box which has a big prize = 1
The number of boxes which have medium prize = 3
The number of boxes which have small prizes = 3
So , the total number of boxes with prize = 7 boxes
And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes
On simplifying , we get
The probability that the box selected will win the prize A = 7 / 8
The probability that the box selected will win the prize A = 0.875
Hence , the probability is 7/8
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