A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
The formula for calculating the confidence interval is expressed as;
[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]
p is the proportion = 61/92 = 0.66n is the sample size = 92z is the z-score at 90% = 1.645Substitute the given parameters into the formula to have:
[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]
Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
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At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?
f (n) = 2.75 + 4.75 + f (n − 1), f (0) = 2.75
f (n) = 4.75 + f (n − 1), f (0) = 2.75
f (n) = 2.75 + 4.75n, n > 0
f (n) = (2.75 + 4.75)n, n > 0
The recursive equation for f(n) will be:
f(n) = 2.75 + 4.75n, n > 0
The cost of the shoe rental = $2.75
The cost of 1 game = $2.75
The cost if n games = 4.75n
The total cost of shoe rental and n games = Cost of the shoe rental + cost of n games
Let the total cost of shoe rental and n games be f(n)
f(n) = 2.75 + 4.75n
Since at least 1 game will be played,
the recursive equation for f(n) will be:
f(n) = 2.75 + 4.75n, n > 0
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Answer: They are inverses of each other
============================================================
Explanation:
We need to check two things:
f(g(x)) = xg(f(x)) = xIf both of those equations are true, then f and g are inverses of each other.
----------------
Part 1
[tex]f(x) = -3x-12\\\\f(g(x)) = -3( g(x) )-12\\\\f(g(x)) = -3\left( \frac{-12-x}{3} \right)-12\\\\f(g(x)) = 12+x-12\\\\f(g(x)) = x\\\\[/tex]
So far, so good. Now we need to check the other equation mentioned.
------------------
Part 2
[tex]g(x) = \frac{-12-x}{3}\\\\g(f(x)) = \frac{-12-( f(x) )}{3}\\\\g(f(x)) = \frac{-12-( -3x-12 )}{3}\\\\g(f(x)) = \frac{-12+3x+12}{3}\\\\g(f(x)) = \frac{3x}{3}\\\\g(f(x)) = x\\\\[/tex]
That works out as well. Both equations mentioned are true, which confirms the two original functions are inverses of one another.
What is the perimeter of the triangle?
Answer:
34
Step-by-step explanation:
12 on two of the sides and 10 on bottom
There is a problem with the question since it is supposed to say how much length does each box in the graph consider. But assuming that each box length is 1 unit...
The pythagorean formula states a^2 + b^2 equals c^2 .... Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
So, lets just divide the blue triangle in half, symmetrically so that we can get a 90 degree angle. "a" is height of the half triangle and "b" is base of the half triangle so we have to find "c" (the hypotenuse) Now that we already can count and find the value of a is 12 unit and b is 5 unit.
So, 12^2 + 5^2 equals c^2 ... now if we solve the formula, the value of "c" comes 13 (it also comes -13 but negative number can not be counted in the diagram)
The triangle is a isoceles triangle which means both the sides of "c" are equal so... one side is 13 then the other side is also 13. and we already know the base is 10 units. So just add them up- 13+13+11 comes 37 units. (Its kinda complicated and i am bad at making someone understand so just learn the pythagorean theorum...)
SO THE FINAL ANSWER IS 37 UNITS. i am not sure so let me know if am correct. And if i m wrong... pls forgive me T-T
(2a+15ab)-(7a+6b-10ab)
Answer:
Step-by-step explanation:
-5a - 6b + 25ab
add like terms
I need help with this badly. It's geometry and angles.
Answer:
∠ C = 118°
Step-by-step explanation:
DE = DF , then Δ DEF is isosceles with base angles congruent , then
∠ DEF = ∠ DFE = [tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62°
∠ DFE and ∠ DFB are adjacent angles on a straight line and sum to 180° , so
∠ DFB = 180° - 62° = 118°
BCDF is a parallelogram ( opposite sides are parallel )
The opposite angles of a parallelogram are congruent , then
∠ C = ∠ DFB = 118°
Here is the list of numbers.
5
11
16
24
29
From the list, write down a multiple of 3.
Plz write down the answer.
Answer:
From the list the multiple of 3 is 24
Solve for x.
5(x−4)2=4x+14
x = 9
x = 8
x=−6
x=−16
Answer:
9 is the answer.
Step-by-step explanation:
5(x − 4)2 = 4x + 14
=> 10x - 40 = 4x + 14
=> 6x = 54
=> x = 9
Therefore, 9 is the answer.
Hoped this helped.
The value of the x after solving the equation 5 (x - 4) 2 = 4x + 14 is x = 9.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given linear equation,
5 (x - 4) 2 = 4x + 14
5 × 2 (x - 4) = 4x + 14
10 (x - 4) = 4x + 14
By distributive property, p (q + r) = p q + p r
10x - (10 × 4) = 4x + 14
10x - 40 = 4x + 14
10x - 4x = 14 + 40
6x = 54
x = 54 / 6
x = 9
Hence the value of x is 9.
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Josh was issued a traffic ticket for speeding. The court cost
was $40 and he had to pay $10 for every mile per hour
over the speed limit. Determine how fast Josh was driving
if the speed limit was 65 mph and his fine was $110.
Answer:
72 mph
Step-by-step explanation:
i did this on achievemath3000 and 72 was the answer
7 grade math hellp mee
Find each key feature of the function shown in the graph. Write the range and domain in interval notation, and assume all values are integers. What's the domain and range for this graph ?
The domain of the graph is [tex]-8<x\leq 9.5[/tex] while the range of the graph is [tex]-4\leq x<4[/tex].
The domain of the graph is input values of "x" for which the function exists while the range is the output values "y" for which the function exists.For the graph, the domain will be the values of the graph along the x-axis.
Domain = [tex]-8<x\leq 9.5[/tex] (Note that -8 is not included)For the range, the interval is given as: [tex]-4\leq x<4[/tex]. Note that the value of 4 is not included since it is opened.Learn more on domain and range here: https://brainly.com/question/1942755
y=sech(tan‐¹x) find the derivative
Recall that
d/dx sech(x) = - sech(x) tanh(x)
d/dx tan⁻¹(x) = 1/(1 + x²)
Then by the chain rule,
dy/dx = - sech(x) tanh(x) / (1 + x²)
(-4x^3-x^2+3)-(x^3-2x^2-7x+2)
[tex](-4x^3-x^2+3)-(x^3-2x^2-7x+2)\\\\=-4x^3 -x^2 +3 - x^3 + 2x^2 + 7x -2 \\\\= -5x^3 +x^2 +7x +1 \\\\=-5x^3 -5x^2 +6x^2 +6x+ x+1\\\\=-5x^2(x+1) +6x(x+1) + (x+1)\\\\=(x+1)(-5x^2 +6x +1)\\\\=-(x+1)(5x^2 -6x -1)[/tex]
If Janet earned e extra credit points. Mona earned 32 fewer extra credit points than Janet.
What is the expression that shows how many extra credit points Mona earned?
How many terms are in the expression?
If a trailer carries 625 gags of cocoa. How many bags will 265 trailers carry?
Answer:
165,625 bags of cocoa.
Step-by-step explanation:
One trailer = 625 bags of cocoa, and if you have 265 trailers it means you will have to multiply 625 by 265.
Which expression is equivalent to squareroot 100?
A10
B10^2
C50
D50^2
Answer:
10^2=100
because all u would do is put down 10 two times and then u just multiply those 2 numbers
Step-by-step explanation:
I don’t understand this question can you please help me ?.
Answer:
Girl: YES = 12 ; NO = 38
Boy: YES = 29 ; NO = 21
Total: YES = 41 ; NO = 59
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
A runner ran 1 4/5 miles on Monday and 6 3/10 on Tuesday. How many times her Monday's distance was her Tuesday's distance? Please help me I need an answer that makes sense
first winter event question: wort 50 points and best explenation wins brainliest
whats 50 x 23 = ? Explain your awenser
Answer:
1150
Step-by-step explanation:
50x 23=150 +100=1150
How many solutions does this system have?
y = 2/3x + 3
2x - 3y = -9
A. one solution
B. two solutions
C. no solutions
D. infinitely many solutions
Answer:
the answer is A .
Step-by-step explanation:
-2x+y=3 ----> 2x - y = -3
6x=9-3y
6x + 3y = 9
divide by 3 ,
2x + y = 3
Since the slopes are different, they will intersect.
So ONE solution.
If f(x)=|x−5|+2, find f(3).
Answer:
4
Step-by-step explanation:
Substitute 3 for x and solve.
|3 - 5| + 2
=|-2| + 2
= 2 + 2 = 4
The line passes through point Q, located at (-1, 2), and point R, located at (1, -2). Which two points determine a line parallel to line Q R ?
Answer:
i need a picture to see sorry
Judith bought a rowboat priced at 671.65.shipping anf handling cost and additional 20% of the prices What was the total cost of the rowboat,including shipping and handilng?
Answer:
805.98
Step-by-step explanation:
671.65x.20=134.33
134.33+671.65=805.98
Help me pls thank you so much
Answer: the second one
Step-by-step explanation:
An electronic company refurbishes game systems The table shows the profit made for the number of game systems sold. How much profit will be made for 35 game systems?
Answer: Give me the table and ill answer..
Step-by-step explanation:
-2.7f + 0.3f - 16 - 4=
Answer:
-2.4f or -8 1/3
Step-by-step explanation:
I am not sure what should be at the end of the equal sign but if it is to simplify it would be -2.4f-20
If you want to solve then you get -2.4f=20 so f=-20/2.4 which equal to -8 1/3
allison made a playlist that included 9/12 country songs. what are two equivalent fractions that represent the part of the play list that is country songs. explain why your fractions are correct?
Answer:
3/4,18/24
Step-by-step explanation:
You can mutiply the numerator and denominator by the same number or divide it by the same number as long as it is a whole number. Ex. (9/3) over (12/3)=3/4. Or (9x2)/(12x2)=18/24
Identify the slope and the y- intercept, as a point (0,b), from the equation.
Y=2/5x-11
Slope -
Y-intercept -
Step-by-step explanation:
Given line:
y = 2/5x - 11Compare this with the slope-intercept form:
y = mx + bThe slope is:
m = 2/5Y-intercept is:
b = - 11As a point on the line it has coordinates (0, - 11)
Answer:
Hope this helps!
Step-by-step explanation:
The slope is:
m = 2/5
Y-intercept is:
b = - 11
The coordinates on the line are: (0, - 11)
A unique source of water pollution contributing to water quality problems in the Ganges River is: A. raw sewage. B. disease-causing organisms. C. zebra mussels. D. PCBs. E. ash from human cremations.
6. (5 points) Graph using two intercepts; show your work in finding the intercepts. 6x - 3y = 18
х
Answer:
Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:
[tex]6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1[/tex] The two intercepts are then 3 and -6.
(I know, dividing by 3 both sides of the equations would have made the whole process way easier).
Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.
Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 1).
Answer:
0.14479638
Step-by-step explanation:
Because 2 cards out of 52 are drawn without replacement, hypergeometric probability distribution should be used. Hence,
Combination of drawing 1 ace of 4 total aces C(4,1)
Combination of drawing 1 non-ace of 48 total non aces C(48,1)
Combination of drawing 2 cards of total 52 cards C(52.2)
C(4,1) = 4, C(48,1) = 48, C(52,2) = 1326
4*48/1326 = 0.14479638