How many men and women should the sample include. What were the steps you took to solve?
Answers
We are asked to determine the sample size to determine the difference in the proportion of men and women who own smartphones with a confidence of 99% and an error of no more than 0.03. If we assume that both samples are equal then we can use the following formula:
[tex]n=\frac{Z^2_{\frac{\alpha}{2}}}{2E^2}[/tex]Where Z is the confidence and E is the error. Replacing the values we get:
[tex]n=\frac{(0.99)^2}{2(0.03)^2}[/tex]Solving the operations we get:
[tex]n=544.5\cong545[/tex]Therefore, each sample of men and women should be of 545.
Related Questions
………………………………………………………….
Answers
you made 66 dots or periods i
think
sin 0 = 1. Find tan 8.A.404141OB. 49O C. 40D.409e
Answers
Because sine is opposite side/ hypotenuse. tangent = opposite angle / adjacent, so we need to find the adjacent side using Pitagora's theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 41^2=9^2+b^2 \\ 1681\text{ - }81=b^2 \\ \sqrt{1600}=b \\ 40=b \end{gathered}[/tex]And now we find tangent.
[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{9}{40}[/tex]So, the correct option is C
Evaluate the expression x2 + 3x for x = −6
Answers
Answer:
30
Step-by-step explanation:
The value of the expression x² + 3x at x = - 6 will be 18.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ x² + 3x
The value of the expression at x = - 6 will be given as,
⇒ (-6)² + 3(-6)
⇒ 36 - 18
⇒ 18
The worth of the articulation x² + 3x at x = - 6 will be 18.
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What is the relationship among proportional relationships, lines, rates of change, and slope? The graph of a (select) unit (select) is a line through the origin whose (select) is the
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The graph of a proportional relationship.
Whose slope
is the unit rate of change
Find the value of the expression when x is 3.x² + 10x + 25
Answers
Given
Expression
[tex]x²+10x+25[/tex]Find
Value of the expression when x = 3
Explanation
Substitute x = 3 in the given expression.
we obtain ,
[tex]\begin{gathered} x²+10x+25 \\ (3)^2+10(3)+25 \\ 9+30+25 \\ 64 \end{gathered}[/tex]Final Answer
Therefore, the value of the expression when x = 3 is 64
What is the approximate length of the edge that Tasha will cover with tile
Answers
Given:
length=16
width=12
radius=4.5
So total length is:
length of half circle is:
circumference of circle:
[tex]\begin{gathered} C=2\pi r \\ \text{half circle=}\frac{2\pi r}{2} \\ =\pi r \end{gathered}[/tex][tex]\begin{gathered} r=4.5 \\ =\pi r \\ =\pi(4.5) \\ =14.137 \end{gathered}[/tex]For there sides of circle is:
[tex]\begin{gathered} \text{length}+\text{width}+\text{width} \\ =16+12+12 \\ =40 \end{gathered}[/tex]for circle side length is:
[tex]\begin{gathered} =16-(\text{diameter of circle)} \\ =16-(2\times4.5) \\ =16-9 \\ =7 \end{gathered}[/tex]So total length is:
[tex]\begin{gathered} =14.137+40+7 \\ =61.137 \\ \approx61 \end{gathered}[/tex]Approximate length of the edge that Tasha will cover with tile is 61.
Kaizen is a Japanese word that means continuous development. It says that each day we should focus on getting1% better on whatever we're trying to improve.How much better do you think we can get in a year if we start following Kaizen today?Note: You can take tilf value of (1.01)365 as 37.78
Answers
If at day 1 we get 1% better than in the day 0, we will be:
[tex]\frac{101}{100}\times1=1.01\times1=1.01[/tex]1.01 better on day 1 than on day 0.
If we get 1% better on day 2 than on day 1, then by day 2 we would be:
[tex]\frac{101}{100}\times1.01=1.01\times1.01=(1.01)^2=1.0201[/tex]1.0201 times better on day 2 than on day 0.
After n days, we would have to multiply 1 by 1.01 n times, so by day n we would be:
[tex]1.01^n[/tex]times better than on day 0.
Calculate 1.01^365 to find how many times better we would be one year after day 0:
[tex]1.01^{365}=37.78343433\ldots[/tex]Therefore, we would get 37.78 times better by day 365, which is after one year.
2.Each year on the same day, Susan deposits $100 into a savings account that earns simple interest at a rate of 3%. She makes no withdrawals. How much interest has Susan’s account earned after 2 years?3.Each year on the same day, Susan deposits $175 into a savings account that earns simple interest at a rate of 3.5%. She makes no withdrawals. How much interest does Susan’s account earn after 5 years?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
P = $100
r = 3% = 0.03
t = 2 years
Step 02:
Simple Interest = P * r * t
= 100 * 0.03 * 2
= 6
The answer is:
Susan earned $6 as simple interest after 2 years.
the volume of the right triangular prism is ______ in3 . use the formula V=Bh
Answers
First, we need to obtain the area of the triangle B
[tex]B=\frac{5\cdot12}{2}=\frac{60}{2}=30in^2[/tex]Then we can use the formula given
[tex]V=\text{ B}\cdot h=30\cdot10=300in^3[/tex]Help me simplify I don’t understand homework and I have to show work .
Answers
The Solution:
Given the expression below:
[tex]\frac{\left(sin\theta+cos\theta\right)^2}{1+2sin\theta\:cos\theta}[/tex]We are required to simplify the above expression.
[tex]\begin{gathered} (\sin \theta+\cos \theta)^2=\sin ^2\theta+2\sin \theta\cos \theta+\cos ^2\theta=\sin ^2\theta+\cos ^2\theta+2\sin \theta\cos \theta \\ =1+2\sin \theta\cos \theta \\ \text{ Since }\sin ^2\theta+\cos ^2\theta=1 \end{gathered}[/tex]So,
[tex]\frac{(sin\theta+cos\theta)^2}{1+2sin\theta\: cos\theta}=\frac{1+2sin\theta\: cos\theta}{1+2sin\theta\: cos\theta}=1[/tex]Therefore, the correct answer is:
[tex]\frac{(sin\theta+cos\theta)^2}{1+2sin\theta\: cos\theta}=1[/tex]Find the mean, median, and mode of the set of data.10, 11, 4, 7, 12, 11, 16, 6, 9, 15
Answers
Before we begin we will order the data set given
4, 6, 7, 9, 10, 11, 11, 12, 15, 16
Mean.
The mean of a data set is given by:
[tex]\operatorname{mean}=\frac{\sum ^{}_{}x_i}{n}[/tex]where the denominator means that we have to add the points on the data and then divide them result by the number of points in the data. In this case we have:
[tex]\begin{gathered} \operatorname{mean}=\frac{4+6+7+9+10+11+11+12+15+16}{10} \\ \operatorname{mean}=\frac{101}{10} \\ \operatorname{mean}=10.1 \end{gathered}[/tex]Hence the mean of the data set is 10.1
Median.
The median is the central value of the ordered data set. In this case we have an even number of values which means that the median is the average of the central values. The central values in this set are the the fifth and sixth term, that is, 10 and 11. The median is then:
[tex]\begin{gathered} \operatorname{median}=\frac{10+11}{2} \\ \operatorname{median}=\frac{21}{2} \\ \operatorname{median}=10.5 \end{gathered}[/tex]Mode
The mode is value that occur most frequently. In this case only the 11 repeats itsefl, hence the mode is 11.
Summing up we have:
Mean 10.1
Median 10.5
Mode 11
Solve the equation: 7+ 3(2x - 1) = (4x+8)
Answers
Fenelon, this is the solution:
Let's solve the equation:
7+ 3(2x - 1) = (4x+8)
1. Solve the parenthesis
7 + 6x - 3 = 4x + 8
2. Like terms:
6x - 4x = 8 + 3 - 7
2x = 4
3. Dividing by 2 at both sides:
2x/2 = 4/2
x = 2
Solved, Fenelon!!
A trapezoid has legs that are 13 cm and 15 cm long. The parallel sides are 11 cm and 25 cm long. The distance between the bases is 12 cm. What is the area of the trapezoid?
Answers
The formula for the area of trapezoid is
[tex]A=\frac{1}{2}\times\sum ^{\square}_{}\text{parallel sides }\times base\text{ height.}[/tex]The area of trapezoid is
[tex]A=\frac{1}{2}\times(11+25)\times12=6\times36=216cm^2[/tex]
Positive numbers are not closed under subtraction. Give an example below.
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A set S is said to be closed under subtraction if:
[tex]\forall a,b\in S,\text{ a-b}\in S\text{ and b-a}\in S[/tex]Since the set given is that of positive numbers, we pick two different positive numbers, say 6 and 9.
[tex]\begin{gathered} \\ 9-6=3\in S \\ 6-9=-3\notin S \end{gathered}[/tex]Since -3 is not a positive number, we can then conclude that the set of positive numbers are
Given the function and the graph below, which of the following best describes the continuity, interval of increase and interval of decrease?
Answers
Given the function:
[tex]f(x)=(-x-1)^2+3[/tex]As we can see, there is no restriction for x, it can be any real value. Additionally, looking at the graph, we do not see any discontinuity ("jumps" or "holes"). We conclude that the function is always continuous.
The vertex of the parabola is at (-1, 3), so x = 1 separates the intervals of increase and decrease. Going from -∞ to -1, we see a decrease in the y-values. Similarly, from -1 to +∞, we see an increment. Then:
Interval of increase: -1 < x < +∞
Interval of decrease: -∞ < x < -1
Find the slope of the line that passes through all of the points
on the table.
X
2
3
4
5
6
Y
3
13
23
33
43
Please help
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In the parallelogram below, if < A = 34 °, what is the measure of < D?
Answers
Given,
The measure of angle A is 34 degree.
Required
The measure of angle D.
It is given that, ABCD is a parallelogram.
According to the property of parallelogram , the opposite sides of the parallelogram are equal and parallel.
The sum of adjacent interior angle between two parallel line is 180 degree.
So,
[tex]\begin{gathered} \angle A+\angle D=180^{\circ} \\ 34^{\circ}+\angle D=180^{\circ} \\ \angle D=146^{\circ} \end{gathered}[/tex]Hence, the measure of angle D is 146 degree.
Misty the cat loved to eat tuna. He wanted to make sure he had enough for the whole week. If misty ate 1\2can of tuna every day,how many cans would he need for a whole week
Answers
Answer:
3.5
Step-by-step explanation:
0.5 * 7 = 3.5
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Find the zeros of the function.7x^2-28=0
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solve for x y and z.
Answers
let us find z
[tex]\begin{gathered} \cos 30=\frac{adjacent}{\text{hypotenuse}} \\ \cos 30=\frac{z}{24} \\ z=24\cos 30 \\ z=20.7846096908 \\ z=20.8 \end{gathered}[/tex]let us find x.
[tex]\begin{gathered} \sin 30=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30=\frac{\text{height}}{24} \\ height=24\sin 30 \\ \text{height}=12 \\ \\ \cos 45=\frac{adjacent}{\text{hypotenuse}} \\ \cos 45=\frac{12}{x} \\ x=\frac{12}{\cos 45} \\ x=\frac{12}{0.70710678118} \\ x=16.9705627485 \\ x=17.0 \end{gathered}[/tex]let us find y
[tex]\begin{gathered} \tan 45=\frac{opposite}{\text{adjacent}} \\ \tan 45=\frac{y}{12} \\ y=12\tan 45 \\ y=12.0 \end{gathered}[/tex]Use the distributive property to expand the expression 3(-3a+4)
Answers
In this case, given 3(-3a+4), -4a+4 are all being multiplied because they are inside the parenthesis. 3 is multiplying-3a+4. So, let’s expand:
3(-3a+4)
3(-3a)+3(4)
-9a+12 is the simplified expression using the distributive property.
solving right triangle find the missing side. round to the nearest tenth number 15
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To solve the triangle we are going to first find the measures of all the angles:
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree}\Rightarrow\text{ Because is a right triangle} \\ A+B+C=180\text{\degree} \\ \text{Because the sum of the internal angles of a triangle is 180 degrees} \\ 47\text{\degree}+90\text{\degree}+C=180\text{\degree} \\ 137\text{\degree}+C=180\text{\degree} \\ \text{ Subtract 137\degree from both sides of the equation} \\ 137\text{\degree}+C-137\text{\degree}=180\text{\degree}-137\text{\degree} \\ C=43\text{\degree} \end{gathered}[/tex]Now to find the measures of the sides you can use trigonometric ratios because it is a right triangle:
Side a: you can use the trigonometric ratio tan(θ)
[tex]\tan (\theta)=\frac{\text{ opposite side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan (47\text{\degree})=\frac{a}{28} \\ \text{ Multiply by 28 from both sides of the equation} \\ \tan (47\text{\degree})\cdot28=\frac{a}{28}\cdot28 \\ 30=a \end{gathered}[/tex]Side b or side x: you can use the trigonometric ratio cos(θ)
[tex]\cos (\theta)=\frac{\text{adjacent side}}{\text{hypotenuse}}[/tex][tex]\begin{gathered} \cos (47\text{\degree})=\frac{28}{b} \\ \text{ Multiply by b from both sides of the equation} \\ \cos (47\text{\degree})\cdot b=\frac{28}{b}\cdot b \\ \cos (47\text{\degree})\cdot b=28 \\ \text{ Divide by cos(47\degree) from both sides of the equation} \\ \frac{\cos (47\text{\degree})\cdot b}{\cos (47\text{\degree})}=\frac{28}{\cos (47\text{\degree})} \\ b=\frac{28}{\cos(47\text{\degree})} \\ b=41.1 \end{gathered}[/tex]Therefore, when solving the triangle you have
[tex]\begin{gathered} A=47\text{\degree} \\ B=90\text{\degree} \\ C=43\text{\degree} \\ a=30 \\ b=41.1 \\ c=28 \end{gathered}[/tex]and the missing side is
[tex]\begin{gathered} b=x \\ x=41.1 \end{gathered}[/tex]A fast food restaurant sold 35 burgerswith cheese. If the ratio of burgers soldwith cheese compared to withoutcheese was 7:3, how many burgers didthey sell total?
Answers
Answer:
The total number of burgers sold is: 50
Problem Statement
The question tells us a restaurant sold 35 burgers with cheese and also that the ratio of burgers sold with cheese compared to burgers sold without cheese is 7:3.
We are asked to find the total amount of burgers sold; with and without the cheese.
SOLUTION
The question already told us that the ratio of burgers sold with cheese to those without cheese is 7:3. This means that for every 7 burgers with cheese sold, the restaurant also sold 3 burgers without any cheese.
This further implies that out of 10 burgers sold at a time, the restaurant must have sold 7 cheeseburgers and 3 burgers without cheese.
This means that we can say:
[tex]35\text{ burgers represent }\frac{7}{10}\text{ of burgers sold by the restaurant}[/tex]If this is the case, then we can also say that:
[tex]\frac{3}{10}\text{ of the total burgers sold is without cheese}[/tex]Thus, we can write an equation stating that "35 burgers plus 3/10 of the total burgers (B) must be equal to the total number of burgers (B)"
This is done below:
[tex]\begin{gathered} 35+\frac{3}{10}\times B=B \\ 35+\frac{3B}{10}=B \\ \text{Multiply both sides by 10} \\ 350+3B=10B \\ \text{Subctract 3B from both sides} \\ 350+3B-3B=10B-3B \\ 350=7B \\ \text{Divide both sides by 7} \\ \frac{350}{7}=\frac{7B}{7} \\ 50=B \\ \\ \therefore B=50 \end{gathered}[/tex]Final Answer
Thus, the total number of burgers sold is: 50
what is the answer to 3+2q+6-q
Answers
To simplify the expression 3+2q+6-q, we have to combine like terms, we do this by combining the terms that are multiplied by the same variable (y) and the terms that are not being multiplied by any variable, we can do it, like this:
3+2q+6-q = (3 + 6) + (2q - q) = (9) + (q) = 9 + q
Then, the answer is 9 + q
What transformations to the linear parent function, f(x) = x, give the functiong(x) = 3x - 1? Select all that apply.A. Horizontally stretch by a factor of 3.B. Shift left 1 unit.nC. Vertically stretch by a factor of 3.UD. Shift down 1 unit.SUBMIT
Answers
We are given a parent function f(x)= x and asked the transformation process that takes it to g(x)=3x-1
PART 1
If g(x) = 3f (x): For any given input, the output g(x) is three times the output of f(x), so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f(x), so the graph is shrunk horizontally by a factor of 3.
In this case, we can state that the function was first stretched by 3.
PART 2
To move a function up, you add outside the function: f (x) + b is f (x) moved up b units. Moving the function down works the same way; f (x) – b is f (x) moved down b units.
We can also say that the function was shifted downwards by 1
ANSWER: OPTION C AND D
7. On the coordinate grid below, show a line that is parallel to y = 2x + 4. 2 5 3 1 2 3 2 -1 4
Answers
Answer
the graph of the line parallel to y = 2x + 4 is presented below
The line has the equation y = 2x + 1
Explanation
Any two parallel lines will have the same slopes.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, for y = 2x + 4, the slope is evidently 2
So, any line that we will pick that will be prallel to the given line has to be of the form
y = 2x + c
c, the y-intercept, can then be any number. Let us use an example where c = 1
The equation of a line parallel to y = 2x + 4 is y = 2x + 1
To plot this, we would need to use the intercepts.
when x = 0,
y = 2x + 1
y = 2(0) + 1
y = 0 + 1 = 1
First point of the line is (0, 1)
when y = 0
y = 2x + 1
0 = 2x + 1
2x = -1
Divide both sides by 2
(2x/2) = (-1/2)
x = -0.5
Second point on the line is (-0.5, 0)
We can then plot the line on the coordinate using these two points (0, 1) and (-0.5, 0)
So, the graph of the line parallel to y = 2x + 4 is presented under 'Answer'
Hope this Helps!!!
First, rewrite8/9 and 7/8so that they have a common denominator
Answers
we have
8/9 and 7/8
9=3*3
8=2*2*2
LCM=9*8=72
therefore
8/9 multiply by 8/8-----> (8/9)*(8/8)=64/72
7/8 multiply by 9/9 ----> (7/8)*(9/9)=63/72
8/9 and 64/72 are equivalent fractions
7/8 and 63/72 are equivalent fractions
If carpeting costs R75,50/m and an entrance hall has a length of 468,cm. Determine the cost of carpenting the hallway?
Answers
The cost of carpeting the hallway is Rs. 35,334.
The cost of carpeting is Rs. 7,550 per meter. We have an entrance hall. The length of the entrance hall is 468 cm. We need to find out the total cost of carpeting the hallway.
First of all, we will convert all the quantities to the same units. The length of the entrance hall is 468/100 = 4.68 meters.
The total cost of carpeting the hallway is the product of the length of the hallway and the cost of carpeting per unit length. Let the cost be represented by the variable "C".
C = Rs. 7,550*4.68
C = Rs. 35,334
Hence, the cost of carpeting the hallway is Rs. 35,334.
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14. Hotel Rates You rent a hotel room for $72 a night. The hotel adds a charge for using its parking lot to the total bill, Afterstaying at the hotel for 3 nights, your total bill is $231.a. Write an equation in slope-intercept form that gives your total bill (in dollars) as a function of the number ofnights you stay in the room.b. How much of your bill was for the parking fee?c.How much does it cost to stay at the hotel for 7 nights?d. If your bill was $591, how many nights did you stay at the hotel?
Answers
Answer:
(a)y=72x+15
(b)$15
(c)519
(d)8 nights
Explanation:
Let the number of nights which you stay = x
The cost of renting a room for a night =$72
Therefore, the costs for x nights = $72x
If the charge for using its parking lot = c
Then, the total cost, y=72x+c
Part A
When the total bill = $231
x=3 nights
[tex]\begin{gathered} 231=72(3)+c \\ 231=216+c \\ c=231-216 \\ c=15 \end{gathered}[/tex]Therefore, an equation in slope-intercept form that gives your total bill as a function of the number of nights, x is:
[tex]y=72x+15[/tex]Part B
Your packing fee, c=$15
Part C
When the number of nights, x=7
[tex]\begin{gathered} \text{Total Cost,y}=72(7)+15 \\ =504+15 \\ =\$519 \end{gathered}[/tex]Part D
When the total cost, y = $591
[tex]\begin{gathered} 591=72x+15 \\ 72x=591-15 \\ 72x=576 \\ \frac{72x}{72}=\frac{576}{72} \\ x=8 \end{gathered}[/tex]If your bill was $591, you stayed for 8 nights.
Identify the polynomial by selecting the most accurate name for the example: 3x² + 6x - 10
Answers
Notice that the degree of the polynomial
[tex]3x^2+6x-10[/tex]is 2. Then it is called a trinomial expression.