a) A sample size of at least 963 drivers is needed.
b) A sample size of at least 753 drivers is needed.
a) To determine the sample size needed for a 90% confidence interval with a margin of error of 3%, we need to use the formula:
[tex]n = (z^2 \times p \times q) / E^2[/tex]
Where:
n = sample size
z = the z-score corresponding to the desired confidence level (in this case, 1.645 for 90%)
p = the estimated proportion of drivers exceeding the speed limit (unknown)
q = 1 - p
E = the margin of error (0.03)
To find the minimum sample size required, we need to estimate p. Since we do not have any previous information, we can use 0.5 as an estimate, which gives:
[tex]n = (1.645^2 \times 0.5 \times 0.5) / 0.03^2 = 962.59[/tex]
b) If previous studies found that 80% of drivers on this road exceeded the speed limit, we can use this value as an estimate for p in the formula above:
[tex]n = (1.645^2 \times 0.8 \times 0.2) / 0.03^2 = 752.45[/tex]
The answer to part (b) is (D) 753.
for such more question on sample size
https://brainly.com/question/20166137
#SPJ11
Can u answer these for me with the work shown
Answer:
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]
[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]
Step-by-step explanation:
Required
Simplify
Solving (1):
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}[/tex]
Factorize the numerator and the denominator
[tex]\frac{x^2(x + 2) -9(x+2)}{x(x^2-x-6)}[/tex]
Factor out x+2 at the numerator
[tex]\frac{(x^2 -9)(x+2)}{x(x^2-x-6)}[/tex]
Express x^2 - 9 as difference of two squares
[tex]\frac{(x^2 -3^2)(x+2)}{x(x^2-x-6)}[/tex]
[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-x-6)}[/tex]
Expand the denominator
[tex]\frac{(x -3)(x+3)(x+2)}{x(x^2-3x+2x-6)}[/tex]
Factorize
[tex]\frac{(x -3)(x+3)(x+2)}{x(x(x-3)+2(x-3))}[/tex]
[tex]\frac{(x -3)(x+3)(x+2)}{x(x+2)(x-3)}[/tex]
Cancel out same factors
[tex]\frac{(x+3)}{x}[/tex]
Hence:
[tex]\frac{x^3 + 2x^2 -9x-18}{x^3-x^2-6x}= \frac{(x+3)}{x}[/tex]
Solving (2):
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2}[/tex]
Expand the numerator and factorize the denominator
[tex]\frac{3x^2 - 6x + x - 2}{x^2(x- 2)}[/tex]
Factorize the numerator
[tex]\frac{3x(x - 2) + 1(x - 2)}{x^2(x- 2)}[/tex]
Factor out x - 2
[tex]\frac{(3x + 1)(x - 2)}{x^2(x- 2)}[/tex]
Cancel out x - 2
[tex]\frac{3x + 1}{x^2}[/tex]
Hence:
[tex]\frac{3x^2 - 5x - 2}{x^3 - 2x^2} = \frac{3x + 1}{x^2}[/tex]
Solving (3):
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}[/tex]
Express x^2 - 9 as difference of two squares
[tex]\frac{6 - 2x}{x^2 - 3^2} * \frac{15 + 5x}{4x}[/tex]
Factorize all:
[tex]\frac{2(3 - x)}{(x- 3)(x+3)} * \frac{5(3 + x)}{2(2x)}[/tex]
Cancel out x + 3 and 3 + x
[tex]\frac{2(3 - x)}{(x- 3)} * \frac{5}{2(2x)}[/tex]
[tex]\frac{3 - x}{x- 3} * \frac{5}{2x}[/tex]
Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]
[tex]\frac{-(x-3)}{x- 3} * \frac{5}{2x}\\[/tex]
[tex]-1 * \frac{5}{2x}[/tex]
[tex]-\frac{5}{2x}[/tex]
Hence:
[tex]\frac{6 - 2x}{x^2 - 9} * \frac{15 + 5x}{4x}=-\frac{5}{2x}[/tex]
Solving (4):
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x}[/tex]
Expand x^2 - 6x + 9 and factorize 5x - 15
[tex]\frac{x^2 -3x -3x+ 9}{5(x - 3)} / \frac{5}{3-x}[/tex]
Factorize
[tex]\frac{x(x -3) -3(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]
[tex]\frac{(x -3)(x-3)}{5(x - 3)} / \frac{5}{3-x}[/tex]
Cancel out x - 3
[tex]\frac{(x -3)}{5} / \frac{5}{3-x}[/tex]
Change / to *
[tex]\frac{(x -3)}{5} * \frac{3-x}{5}[/tex]
Express [tex]3 - x[/tex] as [tex]-(x - 3)[/tex]
[tex]\frac{(x -3)}{5} * \frac{-(x-3)}{5}[/tex]
[tex]\frac{-(x-3)(x -3)}{5*5}[/tex]
[tex]\frac{-(x-3)^2}{25}[/tex]
Hence:
[tex]\frac{x^2 -6x + 9}{5x - 15} / \frac{5}{3-x} = \frac{-(x-3)^2}{25}[/tex]
Solving (5):
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}[/tex]
Factorize the numerator and expand the denominator
[tex]\frac{x^2(x - 1) -1(x - 1)}{x^2 - x-x+1}[/tex]
Factor out x - 1 at the numerator and factorize the denominator
[tex]\frac{(x^2 - 1)(x - 1)}{x(x -1)- 1(x-1)}[/tex]
Express x^2 - 1 as difference of two squares and factor out x - 1 at the denominator
[tex]\frac{(x +1)(x-1)(x - 1)}{(x -1)(x-1)}[/tex]
[tex]x +1[/tex]
Hence:
[tex]\frac{x^3 - x^2 -x + 1}{x^2 - 2x+1}= x +1[/tex]
Solving (6):
[tex]\frac{9x^2 + 3x}{6x^2}[/tex]
Factorize:
[tex]\frac{3x(3x + 1)}{3x(2x)}[/tex]
Divide by 3x
[tex]\frac{3x + 1}{2x}[/tex]
Hence:
[tex]\frac{9x^2 + 3x}{6x^2} = \frac{3x + 1}{2x}[/tex]
Solving (7):
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x}[/tex]
Change / to *
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]
Expand
[tex]\frac{x^2-2x-x+2}{4x} * \frac{12x^2}{x^2 - 2x} * \frac{x}{x-1}[/tex]
Factorize
[tex]\frac{x(x-2)-1(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]
[tex]\frac{(x-1)(x-2)}{4x} * \frac{12x^2}{x(x - 2)} * \frac{x}{x-1}[/tex]
Cancel out x - 2 and x - 1
[tex]\frac{1}{4x} * \frac{12x^2}{x} * \frac{x}{1}[/tex]
Cancel out x
[tex]\frac{1}{4x} * \frac{12x^2}{1} * \frac{1}{1}[/tex]
[tex]\frac{12x^2}{4x}[/tex]
[tex]3x[/tex]
Hence:
[tex]\frac{x^2-3x+2}{4x} * \frac{12x^2}{x^2 - 2x} / \frac{x - 1}{x} = 3x[/tex]
Hello person could you possibly help me with this question?
Answer:
1)whole numbers
2)integers
3)rational numbers
What is the least common multiple of 8, 7, and 2?
Answer:
1 i know its one hope it help
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 2 shows:
2 is prime => 21
Prime Factorization of 7 shows:
7 is prime => 71
Prime Factorization of 8 is:
2 x 2 x 2 => 23
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 7
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 7 = 56
In exponential form:
LCM = 2^3 x 7^1 = 56
LCM = 56
Therefore,
LCM(2, 7, 8) = 56
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Please
Answer:
Step-by-step explanation:
95 divided by 9 please helppppppp
Answer: 95 divided by 9 is 10.5 BUT WITH THE 5 REPEATING
Step-by-step explanation:
The formula for the volume of a cylinder is V=
Answer:
V = pi x radius x 2 x height OR pi x diameter x height
Hope that helps!
Answer:
the formula for the volume of a cylinder is V=πr²h
Simplify.
[tex]m\sqrt{p} + n\sqrt{p} - \sqrt{p}[/tex]
Answer:
First option is the correct answer.
[tex] (m + n - 1) \sqrt{p} [/tex]
Step-by-step explanation:
[tex]m\sqrt{p} + n\sqrt{p} - \sqrt{p} \\ \\ = (m + n - 1) \sqrt{p} [/tex]
Find the measure of the indicated angle to the nearest degree.
PLS URGENT HELP
can someone please help?? what’s the measure of the vertex angle
Answer:
120 deg
Step-by-step explanation:
There is an angle symbol in the equilateral triangle and another symbol in half of the vertex angle. Those two angles are congruent.
The measure of the vertex angle is 2 * 60 deg = 120 deg
Answer: 120 deg
Mr Lee bought 3 packs of meat for barbecue party. Each packs weighed 7 1/2 kg. The price for the meat was $3 pork. How much did Mr Lee bought?
Answer:
68.5
Step-by-step explanation:
each pack 7.5 kg
price for each pack $3
he bought 3
7.5 x 3=22.5
22.5 x3=66.5
El área cuadrada de un tablero de ajedrez mide 1681 cm².¿Cuál es la medida de cada uno de sus lados?
Los lados es = sqrt(1681)
=41cm
a line that passes through the point (2,-1) and has a slope of -3
Answer:
y=3x-7
Step-by-step explanation:
i plotted the point, and used the slope to get the equation
15 points for an answer for this question
Answer:
Is it Khan Academy? You do 5.8 - 2.7 = 3.1
Step-by-step explanation:
Hope that helps!
hi please help i’ll give brainly but please show your work.
Answer:0.028
Step-by-step explanation: 0.07 x 0.4= 0.028
Need help asap !!!!! its math! WI GIVE BRAINLIEST AND A FOLLOW
AND PLEASE SHOW HOW U GOT THE ANSWER Quick
QUESTION:
33 1/3 as a fraction
(3a - 1/2) (3a - 1/2)
Answer: The answer is 9a^2 - 3a + 1/4
Step-by-step explanation:
Hope this helpfull.
But Im so sorry if this not helpfully
Factor: 42x + 14 *
Please help me with this question
Answer:
x = 0.3333333333
Step-by-step explanation:
Simplifying
42x = 14
Solving
42x = 14
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Divide each side by '42'.
x = 0.3333333333
Simplifying
x = 0.3333333333
You deposit $400 Into a bank account. The account pays 2.75% annual interest compounded semi-annually. Find the balance after 5 years
Answer:
$452.56
Step-by-step explanation:
400 * 1.025^(5)
SMART PPL PLEASE HELP MEEEE
Answer:
it's 80% of 125
the value of x = 125
Step-by-step explanation:
14 = 3y - 4
Help me pls
Answer:
y = 6
Step-by-step explanation:
I'm going to assume you want to solve for y.
Step 1: Move all constants to 1 side, isolating y and its coefficient:
14 = 3y - 4
14 + 4 = 3y - 4 + 4
18 = 3y
Step 2: Divide both sides by 3 to solve for y:
3y = 18
3y / 3 = 18 / 3
y = 6
Final answer: y = 6
84 miles in 12 days how many miles a day
Answer:
7 miles per day
Step-by-step explanation:
Solve:
84 divided by 12
Check:
12 multiplied by 7
Hope this helps!
If you were solving 17 x 23 using the area model, which numbers would be partial products you would use to find the product
Answer:
The number to use are 10, 7, 20 and 3.
Step-by-step explanation:
Given
[tex]17 * 23[/tex]
Required
Which numbers would be used using the area model or partial products
The number to use are 10, 7, 20 and 3.
This is shown below:
[tex]\begin{array}{ccc}{ } & {10} & {7} & {20} & { } & { } \ \\ {3} & { } & { } \ \end{array}[/tex]
When the numbers are multiplied, we get:
[tex]\begin{array}{cccc}{ } & {10} & {7} & {} & {20} & {200} &{140} &{=340}\ \\ {3} & {30 } & {21 } &{=51} \ \end{array}[/tex]
[tex]Total = 340 + 51[/tex]
[tex]Total = 391[/tex]
4−2(3+7)=4−23−27
Is this true or fasle
Answer:
false
Step-by-step explanation:
Miss Smith took her bird to the vet 20 weighed 1 and 3/10 pounds the vet said that tweety weighed 4/10 pound more last year how much did tweety way last year
Answer:
1 and 7/10 pounds?
Step-by-step explanation:
because if its 4/10 more you add 3/10 and 4/10 im pretty sure
Answer:
PLEASE MARK BRAInliest
Step-by-step explanation:
tweety weighed 17/10 pounds last year.
if a recipe has 3/8 cups of water and 2 cups of flour what is the ratio and then what is the ratio in a fraction or simplified? PLEASE HELP WITH A REAL ANSWER
Answer: The ratio of eggs, eggs, to two cups of flour. Let me write two cups of flour. Cups of flour. In either case is, is four eggs for every three cups of flour 5/2
Step-by-step explanation: Im not sure through
What is the surface area of this square pyramid? Please help
Find |14.06|= I'm having trouble with this.
Answer:
14.06
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between 0 and 14.06 is 14.06.
Answer:
14.06
Step-by-step explanation:
|14.06| means the absolute value of 14.06, which is 14.06!
Hope that helps!
Which of the following is equvalent to (16^3/2)^1/2
A. 6
B. 8
C. 12
D. 64
Step-by-step explanation:
b 8 is the answer
simplify to2^4^(3/4) then 2^3 then that simplies to 8
help please
15 − 20 + (−15) + (+20)=
Answer:
-5+5
= 0
Step-by-step explanation:
Answer:
-5+5
= 0
Step-by-step explanation:
Evaluate 517 - 91 - 2.
01
-12
00
o
Answer:
its C. 8 :) please give me brainlist