Answer:
See below, please.
Step-by-step explanation:
The rise of democracy has had a significant impact on the African continent, with many countries transitioning from authoritarian rule to democratic governance since the 1990s. For example, South Africa emerged from decades of apartheid and transitioned to democracy in 1994, with the election of Nelson Mandela as the country's first black president. Similarly, in Ghana, the return to multiparty democracy in 1992 after years of military rule led to the establishment of a more stable political system.
The impact of democracy has not been uniform across Africa, with some countries experiencing significant challenges in their democratic transitions. For instance, in Zimbabwe, President Robert Mugabe, who came to power after independence in 1980, held on to power for over three decades through rigged elections and suppression of political opposition. It wasn't until a military coup in 2017 that he was forced to step down.
Despite the challenges, democracy has brought about some significant improvements on the African continent. With democratic governance, there has been a greater emphasis on human rights, the rule of law, and good governance. Free and fair elections have become the norm in many African countries, and citizens have become more involved in the political process, leading to greater accountability from leaders.
The rise of democracy in Africa has had both positive and negative impacts, but overall it has contributed to the establishment of more accountable and transparent governance systems. With democratic institutions in place, African nations are better positioned to address the political and socio-economic challenges that they face.
4. A pet store has eight dogs and cats. Three are dogs. What fraction represents the number of cats?
A. 1/4
B. 3/8
C. 1/2
D.5/8
Answer:
Step-by-step explanation:
Number of cats = 8 - 3 = 5
Fraction that are cats [tex]=\frac{5}{8}[/tex]
rewrite each equation without absolute value for the given conditions
y=|x-3|+|x+2|-|x-5| if 3
Answer:
Step-by-step explanation:
|x-3|=x-3,if x-3≥0,or x≥3
|x-3|=-(x-3),if x-3<0 ,or x<3
What is the slope of the line in the following graph?
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
can you help to solve this two questions?
41.
a=?
b=?
42.
slope of the tangent line=?
The equation of the tangent line to the graph of the function at x = 7 is: y = -1/49 x + 50/343, the equation of the normal line to the graph of the function at x = 7 is: y = 49x - (2402/7) and slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.
What is the tangent line to the graph of the function at x = 7a) To find the tangent line to the graph of the function at x = 7, we need to find the slope of the function at that point. We can use the derivative of the function to find the slope:
f(x) = 1/x
f'(x) = -1/x^2
So, at x = 7, the slope of the tangent line is:
m = f'(7) = -1/7^2 = -1/49
To find the equation of the tangent line, we also need a point on the line. We know that the point (7, 1/7) is on the graph of the function, so we can use that as our point. Using the point-slope form of a line, we have:
y - 1/7 = -1/49(x - 7)
Simplifying this equation, we get:
y = -1/49 x + 50/343
So the equation of the tangent line to the graph of the function at x = 7 is:
y = -1/49 x + 50/343
b) To find the normal line to the graph of the function at x = 7, we need to find a line that is perpendicular to the tangent line we found in part (a). The slope of the normal line is the negative reciprocal of the slope of the tangent line:
m(normal) = -1/m(tangent) = -1/(-1/49) = 49
Using the point-slope form of a line again, we can find the equation of the normal line that passes through the point (7, 1/7):
y - 1/7 = 49(x - 7)
Simplifying this equation, we get:
y = 49x - [(2402)/7]
So the equation of the normal line to the graph of the function at x = 7 is:
y = 49x - (2402/7)
Problem 42:
We can use the limit definition of the derivative to find the slope of the tangent line to the graph of y = 5x^3 at the point (2,40).
Using the formula for the derivative:
dy/dx = lim(h→0) [(f(x+h) - f(x))/h]
we can calculate the slope of the tangent line at x = 2.
Plugging in the given function, we get:
[tex]\frac{dy}{dx} = \lim_{h \to 0} [(5(2+h)^3 - 40) / h][/tex]
[tex]= \lim_{h \to 0} [(40 + 60h + 30h^2 + 5h^3 - 40) / h]\\= \lim_{h \to 0} [60 + 30h + 5h^2]\\= 60[/tex]
Therefore, the slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.
Learn more on slope to the tangent line here;
https://brainly.com/question/6353432
#SPJ1
Please help! 20 points
Order the simplification steps of the expression below using the properties of rational exponents.
Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex] [break the cube root as power [tex]1/3[/tex]]
Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex] [break [tex]875=125\times7[/tex]]
[tex]125=5^3[/tex]
Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex] [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]
Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex] [break the power of [tex]x[/tex]]
Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]
Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]
Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]
Learn more: https://brainly.com/question/20726608
Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
Hi Martin,
To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.
The total purchase cost of all three items is:
Snow shovel: $28.61
Winter coat: $23.27
Rock salt: $7.96
Total purchase cost: $59.84
Now, we apply the applicable taxes:
State tax: 5% of $59.84 = $2.99
County tax: 0.5% of $59.84 = $0.30
City tax: 2.5% of $59.84 = $1.49
Total taxes: $2.99 + $0.30 + $1.49 = $4.78
Therefore, the total purchase price is:
Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62
Which of the following quotients are true? Select all that apply. A. 1 2 ÷ 2 = 4 B. 1 3 ÷ 4 = 4 3 C. 1 2 ÷ 6 = 1 12 D. 1 5 ÷ 2 = 10 E. 1 8 ÷ 3 = 1 24
Answer:
A. 1/2 ÷ 2 = 1/4 is true.
B. 1/3 ÷ 4 = 1/12 is true.
C. 1/2 ÷ 6 = 1/12 is true.
D. 1/5 ÷ 2 = 1/10 is true.
E. 1/8 ÷ 3 = 1/24 is true.
Therefore, all the quotients are true.
(please mark my answer as brainliest)
Find all the values of
arcsin −√3/2
Select all that apply:
a.π3
b.5π6
c.11π6
d.5π3
e.2π3
f.7π6
g.4π3
Answer:
g
Step-by-step explanation:
The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.
Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2
However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.
In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:
sin(π - π/3) = sin(2π/3) = √3/2
This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:
sin(π + π/3) = sin(4π/3) = -√3/2
This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.
Let me know if this helped by hitting brainliest! If you have a question, please comment and I"ll get back to you ASAP!
Answer:
We know that sin(π/3) = √3/2, so we can write:
arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ
where n is an integer.
Therefore, the values of arcsin(-√3/2) are:
a. π/3 + 2nπ
c. 11π/6 + 2nπ
e. 2π/3 + 2nπ
f. 7π/6 + 2nπ
So, options a, c, e, and f are all correct.
seven students are competing in a geography bee. how many ways can they finish in first, second, and third place ?
Answer:
what is the value of x if figure below 80 degree and 50 degree x?
please help!! Given m∥n - find the value of x and y.
(x+19)°
(9x+1)°
(3y+8)°
Answer: x=16, y=9
Step-by-step explanation: Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)
So the two angles add up to 180°
x+19 + 9x + 1 = 180°
combine like terms
10x + 20 = 180
subtract 20
10x = 160
divide by 10
x = 16
Now you can find the measure of the angle marked 9x+1.
9(16) + 1
= 144 + 1
= 145
Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°
3y + 8 + 145 = 180
combine like terms
3y + 153 = 180
subtract 153
3y = 27
divide by 3
y = 9
-Hope this helps! Thanks, have a good day :-)
By what like amount does the length and width of 6 by 4 rectangle need to be increased for its area to be doubled
Answer:
Step-by-step explanation:
Area = 8 x 4 =24
Area doubled = 48
Let x be the amount we increase width and length to get area =48.
[tex](6+x)\times (4+x)=48[/tex]
[tex](x+6)(x+4)=48[/tex]
[tex]x^2+10x+24=48[/tex]
[tex]x^2+10x-24=0[/tex]
[tex](x+12)(x-2)=0[/tex]
[tex]\text{gives }x=-12,2[/tex]
But [tex]x=-12[/tex] is not a practical solution.
So [tex]x=2[/tex] is the required solution.
We must increase the length and width by 2.
(06.04 MC) Jake tossed a paper cup 50 times and recorded how it landed. The table shows the results: Position Open Side Up Closed Side Up Landing on Side Number of Times Landed in Position 2 6 42 Based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). Show your work. (10 points)
To find the experimental probability for each outcome, we divide the number of times the cup lands in that position by the total number of tosses:
Experimental probability of landing open side up = number of open side up landings / total number of tosses = 2/50 = 0.04 or 4%Experimental probability of landing closed side up = number of landings closed side up / total number of tosses = 42/50 = 0.84 or 84%Experimental probability of landing on the side = number of landings on the side / total number of tosses = 6/50 = 0.12 or 12%What is a outcome?
An outcome refers to a possible result of an experiment or event that is used to calculate the probability of that result occurring.
What is meant by experimental probability?
Experimental probability is the probability of an event based on actual, repeated trials or experiments rather than theoretical or mathematical calculations.
To know more about experimental probability visit:
https://brainly.com/question/30694293?referrer=searchResults
#SPJ1
porrect
Question 2
Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Vegan
18
27
45
Male
Female
Total
Meat-eater
0.21
35
37
72
12
23
35
24
14
38
Total
89
101
190
0/1 pts
What is the probability that a randomly selected person is a pescatarian or vegetarian?
Round your answer to the hundredths place.
Answer:
0.38
Step-by-step explanation:
There are a total of 38 pescatarians and 35 vegetarians. This is obtained by looking at the column totals for those categories and includes both males and females
There are a total of 190 participants in the survey
P(pescatarian) = 38/190
P(vegetarian) = 35/190
P(pescatarian or vegetarian)
= P(pescatarian) + P(vegetarian)
= 38/190 + 35/190
= 73/190
= 0.3842
= 0.38 (rounded to hundredths place)
What is 1 2/3 as an improper fraction
Answer:
5/3
Step-by-step explanation:
1×3=3
3+2=5
So answer is 5/3
In the given figure, mHJ = 106° and F H G Figure not drawn to scale FH ~JH. Which statement is true? K 106° J OA. The measure of ZG is 21°, and triangle FGH is isosceles. OB. The measure of ZG is 56°, and triangle FGH is isosceles. OC. The measure of ZG is 21°, and triangle FGH is not isosceles The measure of ZG is 56°, and triangle FGH is not isoscelesd D.
Check the picture below.
[tex]\measuredangle G=\cfrac{\stackrel{far~arc}{148}-\stackrel{near~arc}{106}}{2}\implies \measuredangle G=21^o \\\\\\ \hspace{6em}\measuredangle F=\cfrac{106}{2}\implies \measuredangle F=53^o\hspace{8em}\measuredangle G=106^o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle FGH\textit{ is not an isosceles}~\hfill[/tex]
which of the following is the most appropriate documentation to appear with the calculate procedure?
The documentation "Prints all positive odd integers that are less than or equal to max" is the most appropriate documentation for the printNums procedure, as it accurately describes the behavior of the procedure. so, the option C) is correct.
This procedure uses a loop to display all positive odd integers less than or equal to the input parameter max. It starts by initializing a count variable to 1, and then uses a repeat-until loop to display the current value of count and increment it by 2 until count is greater than max.
The documentation provided is concise, clear, and accurately describes what the procedure does, making it easy for users to understand the purpose and behavior of the procedure. So, the correct answer is C).
To know more about procedure:
https://brainly.com/question/30861505
#SPJ4
_____The given question is incomplete, the complete question is given below:
In the following procedure, the parameter max is a positive integer.
PROCEDURE printNums(max)
{
count ← 1
REPEAT UNTIL(count > max)
{
DISPLAY(count)
count ← count + 2
}
}
Which of the following is the most appropriate documentation to appear with the printNums procedure?
a, Prints all positive odd integers that are equal to max.
b, Prints all negative odd integers that are less than or equal to max.
c, Prints all positive odd integers that are less than or equal to max.
d, Prints all negative odd integers that are less than or equal to max.
What are the x,y axes of equations and the solution
In a school district, 57% favor a charted school for grades K to 5. A random sample of 300 are surveyed and proportion of those who favor charter school is found. Let it be X. What is the probability that less than 50% will favor the charter school? Assume central limit theorem conditions apply.
Which is correct answer?
a
b
c
When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12
Yes, because of the intermediate value theoremWhat is intermediate value theorem?The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.
According to the intermediate value theorem,
since g(x) is a continuous function on the closed interval [1, 6]
since g(1) = 18 is greater than 12, and
g(6) = 11 is less than 12,
there must be at least one value c between 1 and 6 where g(c) = 12.
Therefore, we can conclude that a value of c does exist such that g(c) = 12.
Learn more about intermediate value theorem at:
https://brainly.com/question/30557318
#SPJ1
find the absolute minimuym value of the function over the clsoed triangular region d having vertices g
The absolute maximum is 56 and absolute minimum values is 24 of a function f given by f(x) = 2x³−15x² + 36x +1 on the interval [1, 5] .
A function is defined as a relationship between a set of inputs, each having an output. In short, a function is a relationship between inputs where each input relates to exactly one output. Each function has a domain and a password domain or scope. Functions are usually denoted by f(x), where x is the input.
Given that:
f(x) = 2x³ −15x²+ 36x+ 1
f'(x) = 6x² −30x + 36
Putting f'(x) = 0
⇒ 6x² − 30x+ 36 = 0
⇒ x² −5x+6 = 0
⇒ (x−2)(x−3) = 0
⇒ x=2 or 3
We are given interval [1,5]
Hence, calculating f(x) at 2, 3, 1, 5,
f(2) = 29
f(3) = 28
f(1) = 24
f(5) = 56
Hence, absolute maximum value is 56 at x=5.
Absolute minimum value is 24 at x=1.
Complete Question:
Find the absolute maximum and absolute minimum values of a function f given by f(x)=2x³−15x² + 36x +1 on the interval [1, 5] .
Learn more about Function:
https://brainly.com/question/12431044
#SPJ4
Can anyone help thanks!!!!
Answer:
B
Step-by-step explanation:
5^2 is the small square, 4(3x4x1/2) are the 4 triangles
Answer: The answer would be B.
Step-by-step explanation:
Hello.
First, we know that the smaller square is 5, and to find the area of the big square, we need to square 5 to get the area. We also know that C wouldn't be a viable option, so, our only remaining choices are A and B. We know that without the smaller square, there are 4 triangles, and the Area of a Triangle is: 1/2*b*h. So, this also takes A out as an option as well. After this, you will have your answer as B; 5^2 + 4(3 * 4 * 1/2)
(Or, you could have found the Area of the Triangles, and realize that neither A, nor C have those options, making B the answer by default.)
Hope this helps, (and maybe brainliest?)
A bag with 6 marbles has 2 blue marbles and 4 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in simplest form.
Step-by-step explanation:
Hey mate, if there are no red balls inside the bag then the probabililty will be obviously 0
Each square has a side length of 12 units. Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.
Answer:
The shaded region in all of the answers are equal.
Step-by-step explanation:
Since squares have equal sides, the area of each square is 12 squared or 144.
The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.
The area of the shaded region of A is 144-36pi.
In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.
The area of the shaded region of B is 144-36pi.
In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.
The area of the shaded region of C is 144-36pi.
A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time?
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
Step-by-step explanation:
The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.
A person invests 5,500 dollars in a bank. The bank pays 4.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches $6,700 dollars?
Work Shown:
A = P*(1+r/n)^(n*t)
6700 = 5500*(1+0.045/1)^(1*t)
6700/5500 = (1.045)^t
1.218182 = (1.045)^t
log( 1.218182 ) = log( (1.045)^t )
log( 1.218182 ) = t*log( 1.045 )
t = log(1.218182)/log(1.045)
t = 4.483724
t = 4.5
It takes about 4.5 years to reach $6700
need some help on this question
The value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
Given that, angle F = 90 degrees, angle D = 37 degrees and d = 11 units.
Using the sum of interior angles of triangle we have:
angle F + angle D + angle E = 180
90 + 37 + angle E = 180
angle E = 53 degrees.
Now, using the trigonometric identities we have:
sin (37) = d / f = 11/f
f = 11 / 0.60
f = 18.33
Using tan we have:
tan (37) = d/e = 11 / e
e = 14.59
Hence, the value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.
Learn more about trigonometric functions here:
https://brainly.com/question/6904750
#SPJ1
A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
Learn more: https://brainly.com/question/20521181
The points (-2, -2) and (5,5) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer:
Step-by-step explanation:
[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]
Find the local maximum and minimum values of f using both the first and second derivative tests f(x) = x2 / (x - 1). Summary: The local maximum and minimum values of f(x) = x2 / (x - 1) using both the first and second derivative tests is at x = 0 and x = 2.
The value of local maximum and local minimum for the function f(x) = x^2/(x -1 ) is equal to f(0) = 0 at x = 0 and f(2) = 4 at x = 4 respectively.
Local maximum and minimum values of the function
f(x) = x^2 / (x - 1),
Use both the first and second derivative tests.
First, let's find the critical points of the function,
By setting its derivative equal to zero and solving for x,
f'(x) = [2x(x - 1) - x^2] / (x - 1)^2
⇒ [2x(x - 1) - x^2] / (x - 1)^2 = 0
Simplifying this expression, we get,
x(x - 2) = 0
This gives us two critical points,
x = 0 and x = 2.
These critical points correspond to local maxima, local minima, or neither.
Use the second derivative test,
f''(x) = [2(x - 1)^2 - 2x(x - 1) + 2x^2] / (x - 1)^3
At x = 0, we have,
f''(0) = 2 / (-1)^3
= -2
Since the second derivative is negative at x = 0, this critical point corresponds to a local maximum.
f(0) = 0^2/ (0 -1 )
= 0
At x = 2, we have,
f''(2) = 2 / 1^3
= 2
Since the second derivative is positive at x = 2, this critical point corresponds to a local minimum.
f(2) = 2^2/ (2 - 1)
= 4
Therefore, at x = 0, the local maximum value is f(0) = 0, and at x = 2, the local minimum value is f(2) = 4.
Learn more about local maximum here
brainly.com/question/29560144
#SPJ4
Joan’s finishing time for the Bolder Boulder 10k race was 1.84 standard deviations faster than women’s average for her age group There were 395 women who ran in her age group assuming a normal distribution how many women ran faster than Joan(round down your answer to the nearest whole number)
Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.
What is a whole number?A whole number is a number that is not a fraction, decimal or negative. Whole numbers include all positive integers (1, 2, 3, ...), as well as zero (0). They are also sometimes referred to as counting numbers, as they are commonly used for counting objects or items.
What is standard normal distribution?A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is a specific type of normal distribution that has been standardized to have these specific parameters, which makes it easier to calculate probabilities and perform statistical analyses.
In the given question,
We can use the standard normal distribution to solve this problem. Since Joan's finishing time was 1.84 standard deviations faster than the mean for her age group, we know that her finishing time is in the top (100% - 1.84% = 98.16%) of the distribution.
To find the number of women who ran faster than Joan, we need to find the area under the standard normal distribution curve to the right of her z-score. Using a standard normal distribution table or calculator, we can find that the area to the right of a z-score of 1.84 is 0.0322.
Therefore, approximately 395 x 0.0322 = 12.729 women in Joan's age group ran faster than her. Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.
To know more about standard normal distribution, visit:
https://brainly.com/question/29509087
#SPJ1