Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate is of [tex]\pi = 0.61[/tex], while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2[/tex]
[tex]n = 1015.5[/tex]
Rounding up, 1016 constituents are required.
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Solve the following equations and check your solution using substitution.
5−x=−2
(BTW can you show the working out for the question)
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
We can add the same quantity to both sides of the equations, and still have an equivalent equation. Let's add [tex]x+2[/tex] to both sides, then sum like terms
[tex]5-x +x+2 = -2 +x+2\\5+2 = x\\7=x[/tex]
(this is the rule that allows us to move items from one side do the other of the equal sign by changing its sign)
At this point we have a solution, let's replace it to verify
[tex]5-(7) = -2\\-2=-2[/tex]
A large automobile manufacturing plant produces 1200 new cars every day. a qualitycontrol inspector checks a random sample of 90 cars from one day’s production and finds that 12 of them have minor paint flaws. calculate and interpret a 99% confidence interval for the proportion of all cars produced that day with minor paint flaws.
Using the z-distribution, it is found that the 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are given by:
[tex]n = 90, \pi = \frac{12}{90} = 0.1333[/tex]
Then, the bounds of the interval are found as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 - 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.041[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 + 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.2256[/tex]
The 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.
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In 2001 Arnold was x years old. Ken is 34 years younger than Arnold. In 2013 Arnold is three times as old as Ken. Write down an equation in x and solve it.
Answer:
x = 54
Step-by-step explanation:
x/3 = x-36
x= 3x-36.3
2x= 36.3
x = 18.3
x = 54
Answer:
(x +12) = 3((x -34) +12)x = 39Step-by-step explanation:
The given age ratio is valid 12 years after the age at which Arnold was x years old. When Arnold was x, Ken was x-34.
(x +12) = 3((x -34) +12) . . . . . the age relation in 2013
__
Solving for x, we have ...
x +12 = 3x -102 +36
78 = 2x . . . . . . . add 66-x
39 = x
In 2001, Arnold was 39 years old.
_____
Additional comment
In 2001, Arnold was 39 and Ken was 5. Ken is 34 years younger.
In 2013, Arnold was 51 and Ken was 17. Arnold was 3 times Ken's age.
If the circumference of a circle is 88 cm find its area
What is the length of PR?
Answer:
c 6
Step-by-step explanation:
since angles are equal then the sides can be equal
(AB÷PQ)=(AC÷PR)
(20÷5)=(24÷X)
4=24÷X
X=6
The maroon team and the orange team played a game of football. The maroon team scored 30 points and the orange team scored 9 points. What is the ratio of points scored by the maroon team to points scored by the orange team?
Answer:
30:9 or if you want it simplified 10:3
Step-by-step explanation:
Help if you understand please and thanks
Answer:
y = 4
Step-by-step explanation:
because 5 x 4 = 20 and 20 × 4 = 80 and so on y is equal to four
Scientists were studying snakes by catching, tagging, and releasing 77 snakes. A month later, the scientists come back and catch 11 snakes, of which 7 are tagged. Assuming that the catch is representative, how many snakes are there?
Omega House Family restaurant is midway between Forsyth Tech Community College
and the Dash baseball stadium. The coordinates of Forsyth Tech are (7, −5) and the
coordinates of the Dash baseball stadium are (−4, 3). What are the coordinates of the
Omega House?
The coordinates of Omega house is (3/2, 1)
Data;
Forsyth Tech = (7,-5)Stadium = (-4, 3)Midpoint of a LineTo find the coordinates of Omega house, we can use the formula of midpoint of a line since Omega house falls between Forsyth Tech and Stadium
[tex]x,y = (\frac{x_1+ x_2}{2} , \frac{y_1+y_2}{2})[/tex]
We can substitute the values and solve for both x and y coordinates.
[tex]x = \frac{x_1+x_2}{2} \\x = \frac{7 + (-4)}{2} = \frac{3}{2}[/tex]
The value of the y-coordinate is
[tex]y = \frac{-5+ 3}{2} = 1[/tex]
The coordinates of Omega house is (3/2, 1)
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The perimeter of an equilateral triangle is p and the length of a side is s.
The formula for s is s = p = 3
Find the length of a side when the perimeter is 21 cm. = cm
Write down a formula for p in terms of s. p =
Answer:
s=7
p=3s
Step-by-step explanation:
The perimeter is the side length times 3
So the equation would be p=3s
Plug in 21 for p
21=3s
That means s=7
HELP PLEASE
What is the surface area of this right triangular prism?
Enter your answer in the box.
in²
The surface area is the sum of the areas of the faces of a figure. We can break this figure down into 3 different shapes: the base rectangle, the rectangles that come to a point, and the two triangles.
Area of a Rectangle = base x height
Area of a Triangle = 1/2 x base x height
Base rectangle = 24 x 12 = 288
Rectangles that come to a point = 2(12 x 13) = 2(156) = 312
---There are two rectangles, which is why I multiplied the area by 2.
Triangles = 2(1/2 x 24 x 5) = 2(1/2 x 120) = 2(60) = 120
Surface Area = sum of all the areas of the faces
Surface Area = 288 + 312 + 120 = 720 in^2
Answer = 720 in^2
Hope this helps!
In circle S with the measure of arc \stackrel{\Large \frown}{RT}= 156^{\circ} RT ⌢ =156 ∘ , find \text{m} \angle RSTm∠RST
The measure of arc RT in the circle S is about 60 degrees.
What is a circle?A circle is the locus of a point such that the distance from its fixed point is always constant.
The question is not complete. A similar question is attached.
From the diagram:
arc RT = 2 * ∠RUT(angle at circle center is twice angle at circumference)
arc RT = 2 * 30
arc RT = 60°
The measure of arc RT in the circle S is about 60 degrees.
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a. 23,320ft
b. 5,830 ft
c. 11 660 ft
d. 18,000 ft
Answer:
Step-by-step explanation:
D 18,000
The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4. 9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground
Using the given function, it is found that the projectile hits the ground after 20 seconds.
When does the projectile hits the ground?It hits the ground when it's height, given by h(t), is equals to zero.
In this problem, the function that models it's height is given by:
h(t) = -4.9t^2 + 98t.
Then:
h(t) = 0
-4.9t^2 + 98t = 0.
-4.9t(t - 20) = 0
t - 20 = 0 -> t = 20.
The projectile hits the ground after 20 seconds.
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The circle below is centered at (10, 4) and has a radius of 4. What is its equation? A. (x - 10)2 + (y - 4)2 = 16 B. (x - 10)2 + (y - 4)2 = 4 C. (x - 4)2 + (y - 10)2 = 4 D. (x - 4)2 + (y - 10)2 = 16
Answer: A
Step-by-step explanation:
a) what is average rate of change of f(x) over the interval from x=5 to x=9? (table shows values of f(x). graph shows function of g(x).)
table:
x: 4, 5, 6, 7, 8, 9, 10
F(x): -8, -4, 8, 10, 11, 14 ,18
b) Find the average rate of change of g(x) over the interval from x = 0.25 to x= 1. (Write answer as a simplified fraction. Show work)
c) if g(x) represents the height of a ball that was throw. up into the air, interpret your answer from part b) in terms of the real-world it represents.
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A
The average rate of change of a function over the interval [tex][a,b][/tex] is equal to [tex]\frac{f(b)-f(a)}{b-a}[/tex], hence:
[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}[/tex]
Therefore, the average rate of change of [tex]f(x)[/tex] over the interval [tex][5,9][/tex] is [tex]\frac{9}{2}[/tex].
Part B
Do the same thing as in Part A:
[tex]\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4[/tex]
Therefore, the average rate of change of [tex]g(x)[/tex] over the interval [tex][0.25,1][/tex] is [tex]-4[/tex].
Part C
To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).
The average rates of change are:
a) 4.5b) -4c) It means that in the interval, for each second that passes the height decreases by 4ft.How to get the average rate of change?
For a function f(x), the average rate of change on the interval [a, b] is:
[tex]r = \frac{f(b) - f(a)}{b -a}[/tex]
a) Here we have:
[tex]r = \frac{F(9) - F(5)}{9 - 5} = \frac{14 - (-4)}{4} = 4.5[/tex]
b) Now we look at g(x) on the interval [0.25, 1]
Notice that g(0.25) = 5 and g(1) = 2
Then we have:
[tex]r = \frac{2 - 5}{1 - 0.25} = -4[/tex]
c) That average rate of change means that, in average, in that interval in each second the height decreases by 4 ft.
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PLEASE ANSWER I NEED MY MATH GRADE UP PLEASE GUYS
The prism below is made of cubes which measure of an inch on one side. What is the volume?
Note: Figure is not drawn to scale.
A. 12 cubic in
B. 24 cubic in
C. 3 cubic in
D. 9/2 cubic in
on a blueprint, the area of a tennis court is 16.25cm². a) if the scale on the blueprint is 1cm: 4m, what is the actual area of the tennis court? b) if the length of the tennis court on the blue priny is 6.25 cm what it the actual length of the tennis court
Step-by-step explanation:
so,
1cm : 4m
that means the factor is 1/400 (as 1 m = 100 cm).
also to remember : 1 m² = 100cm×100cm = 10,000 cm²
the area of a rectangle is
length × width
if both dimensions are shortened by a factor (1/400) in our case :
length×1/400 × width×1/400 =
= length × width × 1/400² = length × width × 1/160,000
that means the area of the actual tennis court is
160,000 times the area of the blueprint picture :
160,000 × 16.25 = 2,600,000 cm² = 260 m²
we now know that the actual length of the tennis court is 400 times the length of the blueprint length :
400 × 6.25 = 2,500 cm = 25 m
Can pls someone help me? and show how it did it?
Answer:
[tex]x\geq -3[/tex]
Step-by-step explanation:
We can start by combining like terms:
[tex](3x-7x)+(-5+2)\leq 9\\-4x-3\leq 9[/tex]
We want to isolate x, so we must add 3 and divide by -4:
[tex](-4x-3\leq 9)+3\\(-4x\leq 12)/-4\\\\x\geq -3[/tex]
Because we had to divide by -4, the inequality sign had to flip.
Hi please help me out and add an explanation if u can!
What do we know
-the pentagon is a regular pentagon meaning all its side lengths
are equal since all the sides have one tick mark which says all
the side lengths are equal
2. Solve:
Perimeter: 6 + 6 + 6 + 6 + 6 = 30cm
Question 2: Find the height of the prismHeight of the prism
⇒ distance between the base pentagon and the top pentagon
⇒ Height is 6 cm
Question 3: Find the Lateral AreaDefinition of Lateral Area: it is only the area of the non-base faces
⇒ the non-base faces are the squares on the side of the figure
⇒ there are 5 squares
⇒ Lateral Area = 5 * (Area of Square) = 5 * (6 * 6) = 180 square cm
Question 4: Find the area of the base
The formula for the pentagon's area ⇒ [tex]\frac{5}{2}*s*a[/tex]
s --> length of the sides of the pentagon --> 6cma --> apothem length --> 4.1 cm*apothem is the distance from the center of the pentagon to any
one of the sides
Area = [tex]\frac{5}{2} *6*4.1 = 15 * 4.1 =[/tex] 61.5 square centimeters
Question 5: Find the surface areaDefinition of Surface Area: all the areas of different sides added upSurface Area = 2 * (Area of Base) + (Lateral Area)
= 2 *61.5 + 180 = 123 + 180 = 303 square centimeters
Hope that helps!
HEELPPPP ILL GIVE BRAINLIEST
Billy invested $1000.00 into a savings account on the day his daughter was born. The money is being saved for her college tuition. Billy leaves the money in a savings account until his daughter's 18th birthday. The account earned a simple interest rate of 6.925%. What is the total amount in the account?
Answer:
Let the amount invested at 3% = x
Let the amount invested at 6% = y.
From the total amount invested, we get this equation.
x + y = 18
Now we look at the interest earned.
The 3% account earns 0.03x
The 6% account earns 0.06y
5% on the entire amount is 0.05 * 18 = 0.9
This gives us the second equation.
0.03x + 0.06y = 0.9
Now we have a system of 2 equations in 2 unknowns.
x + y = 18
0.03x + 0.06y = 0.9
Solve the first equation for y:
y = 18 - x
Replace 18 - x for y in the second equation.
0.03x + 0.06y = 0.9
0.03x + 0.06(18 - x) = 0.9
0.03x + 1.08 - 0.06x = 0.9
-0.03x + 1.08 = 0.9
-0.03x = -0.18
x = 6
Answer: He invested $6 at 3%
12% of what number is 96? Enter your answer in the box.
Answer:
800
Step-by-step explanation:
96/12=8
8 x 100= 800
Answer:
Your answer is 800
Step-by-step explanation:
A straight line p through A(-2,1) and B(2,k) the line is perpendicular to a line 3y + 2x =5. Determine the value of k
Answer:
k = 7
Step-by-step explanation:
To solve this, first, you need to find the slope of the line. To do this, you can convert it into point-slope form.
3y = -2x + 5
y = - 2/3x + 5/3
The slope is -2/3, so the perpendicular slope in 3/2
You find the difference between the x - values (2 - -2 = 4), then multiply that by the slope (4 x 3/2 = 6) finally, you add that to the y value of point one.
1 + 6 = 7
Please help me!!
If there is an equation let's say
15y = 6/x
Can you multiply 15y by 6
to get 15/6y=x
Or do you need to multiply by x and divide by 15
Answer:
Yes Girlie, you need to multiply by x and divide by 15!!!!!!!!!
Step-by-step explanation:
a dogs leash is tied to a pole while the owners go into a resturaunt to get the dog some water. if the leash is 7 ft long, and hte dog can walk 180 degrees in a semi circle, how many feet can he walk if he extends the leash as far as it can go.
Answer: 22 ft
Step-by-step explanation:
The path that the dog can walk if he maximally extends his leash is the path of a semi-circle, which has a radius of 7ft.
The distance along a full circle is given by the circumference of the circle, which is related to the radius. To find the length of the path that the dog walks, we evaluate half the circumference.
[tex]\begin{aligned}&D=\frac{C}{2} \\&D=\frac{2 \pi r}{2} \\&D=\pi r \\&D=7 \pi \\&D \approx 22\end{aligned}[/tex]
Therefore, the dog can walk about 22 ft if he extends the leash as far as it can go.
2x+2y=6 3x-y=5 equivalent equation
Answer:
x = 2, y = 1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}2x+2y=6\\ 3x-y=5\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Isolate\;x\;for\;2x+2y=6:x=3-y}[/tex]
[tex]\mathrm{Substitute\:}[/tex]
[tex]\begin{bmatrix}3\left(3-y\right)-y=5\end{bmatrix}[/tex]
[tex]\mathrm{Simplfy}[/tex]
[tex]\begin{bmatrix}9-4y=5\end{bmatrix}[/tex]
[tex]\mathrm{Isolate\;y\;for\;9-4y=5:y=1}[/tex]
[tex]\mathrm{For\:}x=3-y\;\mathrm{Substitute\:}y=1[/tex]
[tex]x=3-1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{The\:Answers\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=1[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check Answer:
Since [tex]x =2 , y =1[/tex]
[tex]2(2)+2(1)[/tex]
[tex]4 + 2[/tex]
[tex]= 6[/tex]
True
[tex]3(2) - (1)[/tex]
[tex]6 -1[/tex]
[tex]5[/tex]
True
Hence, [tex]x = 2, y = 1[/tex]
~Lenvy~
PLS HELP ILL MARK AS BRAINLIEST PLSS
Answer:
10%
Step-by-step explanation:
I think it's right lol but I could be wrong I forgot a lot of this stuff
but out of all the data it goes from 22-42 so 20 points in total
there is only 2 of the data points behind 24, so it is 2/20 or 10%
Karen has just baked 17 cookies. She wants to put them in paper bags in groups of 6. How many groups of 6can she make ? How many cookies will she have remaining ?
Answer:
She can make 2 groups of six, with five cookies remaining
Step-by-step explanation:
First, divide 17 by 6 to get 2 5/6. The whole number is the number of groups she can make, and the fraction is how many are left over. She can make two groups, with five left over.
Hopefully this helps - let me know if you have any questions!
Answer:
2 groups with 5 left over.
Step-by-step explanation:
to solve, take 17 and divide it by 2. since we only have 17 cookies, we round down no matter what. to get the left over, multiply 2 by 6, then subtract by 17.
please mark as brainlest.
An expression is given
3(3 squared2 -4)
Answer:
0.728 to nearest thousandth.
Step-by-step explanation:
3(3 squared2 -4)
= 9√2 - 12
= 0.728 to nearest thousandth.
Solve: 2x + 3 = -1
Please help me on this question :)
Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.
What is an Equation?An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.
Given the data in the question;
2x + 3 = -1Value of x = ?2x + 3 = -1
First, we collect like terms.
2x = -1 - 3
2x = -4
divide both sides by 2
2x/2 = -4/2
x = -4/2
x = -2
Given that 2x + 3 = -1 is a mathematical formula that expresses the equality of two expressions, the value of x in the equation is -2.
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