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.
Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
Which construction is shown in the diagram below?
Answer:
Step-by-step explanation:
i think it B
What is the period of f(x)=secx?
Enter your answer in the box.
period of f(x)=secx:
Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.
What is function?The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.
Here,
=> F(x) = sec(x) has a 2 phase.
Because the secant function is periodic, its values recur after a predetermined amount of time.
This interval's length is equal to the secant function's duration.
The formula for the secant function is
=> sec(x) = 1/cos.(x).
The cosine function repeats its values every 2 units of x, which is known as its period.
Consequently, the secant function has a period of 2 as well.
Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.
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TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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A candy store owner used a cylindrical wooden log as a bench in their store. The height
of that log was 2
feet. The diameter of its base was 1.25
feet. If it costs $7.20
per square foot to paint that log at every side, how much approximately will it cost the
store owner? The total surface area of the right circular cylinder is 2nrh+2rr2
, where, r
is the radius of the base of the cylinder and, h
is the height of the cylinder
Answer:
Step-by-step explanation:
its 60
if the area to the left of x in a normal distribution is 0.123, what is the area to the right of x? [1 point]
The area to the right of x is 0.877.
In a normal distribution, the entire area under the curve is identical to 1. The area to the left of a specific value of x represents the possibility of observing a value largely lesser than or same tox.
However, we're capable to discover the area to the right of x with the aid of abating the left area from 1, If the place to the left of x is given.
In this case, the area to the left of x is 0.123. thus, the place to the right of x is
1-0.123 = 0.877
Thus, the area is 0.877 to the right of x.
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spinner is divided into seven equal sections numbered 1 through 7 If the spinner is spun twice, what is the theoretical probability that it lands on 2 and then an odd number?
A) 1/49
B) 4/49
C) 1/7
D) 4/7
Answer:
B is correct
Step-by-step explanation:
If it is spun twice then the probability of it landing on 2 and then an odd number is:
Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)
1/49 * 4
4/49
your friend claims the geometric mean of 4 and 9 is 6, and then labels the triangle, as shown. is your friend correct? explain your reasoning.
The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.
Explain about the geometric mean?An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.
Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.
For the given question.
geometric mean of a and b :
From the drawn diagram.
a = 4
b = 9
x = √ab
x = √9*4
x = 6
geometric mean: 6
Applying the altitude rule:
h² = x.y
6² = 9*4
36 = 36
Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.
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PLEASE HELP FAST!!
Find the slope of a line perpendicular to the line whose equation is
4x−6y=−24. Fully simplify your answer.
Answer: -3/2
Step-by-step explanation:
FIrst rearrange the equation in y = mx + b form.
4x - 6y = -24
-6y = -4x - 24
y = 2/3x + 4
If the line is perpendicular, the slope must be the negative reciprocal of the current line.
The negative reciprocal of 2/3 is -3/2.
consider a student loan of $15000 at a fixed APR of 12 % for 20 years
Therefore, the monthly payment for a student loan of $15,000 at a fixed APR of 12% for 20 years is $144.36.
What is interest?Interest is the cost of borrowing money or the return on investing money. When you borrow money, you usually have to pay back more than you borrowed, and the additional amount you pay is the interest. The interest rate is expressed as a percentage of the borrowed amount, and it can vary depending on factors such as the borrower's credit score, the term of the loan, and the lender's policies.
Given by the question.
Assuming the loan has a fixed interest rate of 12% per annum, the amount of interest charged each year will be:
12% of $15,000 = $1,800
The total interest charged over 20 years will be:
$1,800 x 20 = $36,000
The total amount to be repaid (principal + interest) will be:
$15,000 + $36,000 = $51,000
If the loan is being repaid in equal monthly installments over the 20-year term, the monthly payment can be calculated using the following formula:
M = P * (r[tex](1+r)^{n}[/tex]) / ([tex](1+r)^{n}[/tex]- 1)
Where:
M = Monthly payment
P = Principal amount (in this case, $15,000)
r = Monthly interest rate (12% per annum / 12 months = 1% per month)
n = Total number of payments (20 years x 12 months per year = 240)
Plugging in the values:
M = $15,000 * (0.01[tex](1+0.01)^{240}[/tex]) / ([tex](1+0.01)^{240}[/tex] - 1)
M = $144.36
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Work out the size of angle x. 79°) 35
Answer: 66
Step-by-step explanation:
all 3 of them should equal to 180
so 79+35 is 114
180-114 will give us the answer which is 66
What is the solution for those?
And if you can please add the explanations
The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.
What is Equation?the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.
According to question:Simplified forms of the equation are
[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]
[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]
[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]
[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]
f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]
[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]
[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]
[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]
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Let f(x) = x? - 6x + 8 and g (x) = x - 5.
Find (f + g) (x) and (f - g) (x) .
What is the end behavior of the polynomial function?
Answer: D. As x → -∞, y → -∞.
Step-by-step explanation:
The graph shows the function approaching negative infinity on the x-axis (left side). When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.
please help!!! i really need it
Step-by-step explanation:
Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:
$25 - $22.90 = $2.10
We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:
$2.10 ÷ $0.14/yd = 15 yards
Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.
can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
State if the triangles in each pair are similar
Answer:
They are similar
Step-by-step explanation:
It's because 27/18 = 12/8
27/18 = 1.5
12/8 = 1.5
A cylindrical aluminum can is being constructed to have a height h of 7 inches. If the can is to have a volume of 56 cubic inches, approximate its radius r. (Hint: V = 2²h)
The radius of the can is about _ inches.
(Type an integer or decimal rounded to two decimal places as needed)
When rounded to two decimal places, the radius of the can is approximately 1.6 inches.
What exactly is a cylinder?Surface fοrmed by a straight line mοving parallel tο a fixed straight line and intersecting a fixed planar clοsed curve. a sοlid οr surface defined by a cylinder and twο parallel planes that cut all οf its elements. See Vοlume Fοrmulas Table, particularly fοr the right circular cylinder.
The volume of a cylinder can be calculated using the following formula:
V = πr²h
where
V denotes volume,
r denotes radius, and
h denotes height.
The cylindrical aluminium can has a height of 7 inches and a volume of 56 cubic inches. We can calculate the radius using the volume of a cylinder formula:
V = πr²h
56 = πr²(7)
56 = (22/7)r²(7)
56 = 22r²
56/22 = r²
2.54 = r²
r = [tex]\sqrt{2.54}[/tex]
r ≈ 1.6
As a result, when rounded to two decimal places, the radius of the can is approximately 1.6 inches.
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When you calculate (In) 7, you would be finding the
value of which of the following expressions?
O log10 7
O log, 10
O log, e
O log 7
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
what is logarithm?In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).
When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).
As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).
Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.
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find the standard form of the equation of the ellipse having foci (2,0) and (2,6) and a major axis of length 8
The standard form of the equation of the ellipse is (x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
To find the standard form of the equation of the ellipse, we first need to determine some of its properties.
The foci of the ellipse are given as (2, 0) and (2, 6). This tells us that the center of the ellipse is at the point (2, 3), which is the midpoint of the line segment connecting the foci.
The major axis of the ellipse is given as a length of 8. Since the major axis is the longest dimension of the ellipse, we can assume that the length of the major axis is 2a = 8, so a = 4.
Next, we need to determine the length of the minor axis. We know that the distance between the foci is 2c = 6, so c = 3. Since c is the distance from the center of the ellipse to each focus, we can use the Pythagorean theorem to find the length of the minor axis
b^2 = a^2 - c^2
b^2 = 4^2 - 3^2
b^2 = 7
b = sqrt(7)
Now we have all the information we need to write the standard form of the equation of the ellipse. The standard form is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) is the center of the ellipse. Plugging in the values we found, we get
(x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
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How many proper subsets are in {2,4,6,8...100}
Answer:
159 proper subsets.
Step-by-step explanation:
Given a set {2, 4, 6, 8...100}, how many proper subsets are there?
First, find how many subsets there are in 2 - 10:
That's 16.
Then because there are 10 10s in 100, multiply by 10:
16 x 10 = 160
Finally, because it says proper subsets, subtract by 1:
160 - 1 = 159 proper subsets.
Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}
PLEASE HELP
The linear function f(x) = 0.9× + 79 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
The required answers are 80.8, 79,and g(42) > f(42).
How to find average of equation?Part A:
To determine the test average for the math class after completing test 2, we need to evaluate the function f(x) at x=2. That is,
[tex]$$f(2) = 0.9(2) + 79 = 80.8$$[/tex]
Therefore, the test average for the math class after completing test 2 is 80.8.
Part B:
To determine the test average for the science class after completing test 2, we need to find the equation of the linear function g(x) that passes through the given points (1,78) and (2,79). The slope of the line passing through these points is
[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{79-78}{2-1}=1$$[/tex]
We can use the point-slope form of a line to find the equation of the line passing through the point (1,78) with slope m=1. That is,
[tex]$$y-78 = 1(x-1)$$[/tex]
Simplifying, we get
y = x + 77
Therefore, the test average for the science class after completing test 2 is
g(2) = 2 + 77 = 79
Part C:
To determine which class had a higher average after completing test 42, we need to evaluate f(42) and g(42) and compare the results. We have
[tex]$$f(42) = 0.9(42) + 79 = 117.8$$[/tex]
To find (42), we need to extend the linear function g(x) beyond the given data points by assuming that the function is linear and continues with the same slope m=1. That is,
g(x) = x + 77
for all [tex]$x\geq 1$[/tex]. Therefore,
[tex]$$g(42) = 42 + 77 = 119$$[/tex]
Since g(42) > f(42), we conclude that the science class had a higher average after completing test 42.
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please help with finding the answer
The answer of the given question based on the transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².
What is Function?In mathematics, function is relation between set of inputs and set of possible outputs with property that each input is related to exactly one output. It is rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.
a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.
b. The equation of the function is y = -2(x+3)².
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Converting from decimal to non-decimal bases. info About A number N is given below in decimal format. Compute the representation of N in the indicated base. (a) N = 217, binary. (b) N = 99, hex. (c) N = 344, hex. (d) N =136, base 7. (e) N = 542, base 5. (f) N = 727, base 8. (g) N = 171, hex. (h) N = 91, base 3. (i) N = 840, base 9.
Hence the conversion of given numbers according to given demand is
a) N=217 in binary = 11011001
b) N=99 in hexadecimal = 63
c) N= 344 in hexadecimal = 158
d) N= 136 in base 7 = 253.
e) N= 542 in base 5 = 4132.
f) N= 727 in base 8= 1327
g) N= 171 in hexa =1011
h) N=91 in base 3=10101.
i) N= 840 in base 9 = 1133
a) A good method to convert a decimal number to binary is dividing it by 2 and using the remainder of the division as the converted number, starting by the most significant bit (the right one). We can't divide anymore. So we have:
217÷2 = 108 + 1
108÷2 = 54 + 0
54÷2 = 27 + 0
27÷2 = 13 + 1
13÷2 = 6 + 1
6÷2 = 3 + 0
3÷2 = 2 +1
2÷2 = 1
The binary equivalent to 217 is 11011001
b) To convert a number from decimal to hex we can divide the number by 16, taking out the decimal part and multiplying it by 16 using that as our most significant number while using the result of the original division to continue our conversion. So we have:
99÷16 = 6.1875
The decimal part is 0.1875, we multiply it by 16 and obtain 3 as our most significant number. Since we can't divide 6 by 16 we have that as our least significant number then the hexadecimal equivalent is 63.
c) We follow the same steps as in item b:
344÷16 = 21.5
The most significant number is 0.5*16 = 8
21÷16 = 1.3125
The next number is 0.3125*16 = 5
Since we can't divide it anymore we have our result which is 158 in hex.
d) To convert from decimal to base 7 we'll use the same method as to hex, but this time dividing and multiplying by 7.
136÷7 = 19.428571
The most significant number is 0.428571 * 7 = 3
19÷7 = 2.71428571
The next number is 0.71428571*7 = 5
Since we can't divide it anymore we have our result which is 253.
e) To convert from decimal to a base 5 we'll use the same method as before but dividing and multiplying by 5.
542÷5 = 108.4
The most significant number is 0.4*5 = 2
108÷5 = 21.6
The next number is 0.6*5 = 3
21÷5 = 4.2
The next number is 0.2*5 = 1
Since we can't divide it anymore we have our result which is 4132.
f) To convert from decimal to a base 8 we'll use the same method as before but dividing and multiplying by 8.
727÷8 = 90.875
The most significant number is 0.875*8 = 7
90÷8 = 11.25
The next number is 0.25*8 = 2
11÷8 = 1.375
The next number is 0.375*8 = 3
Since we can't divide anymore we have our result which is 1327
g) Following the same steps as before:
171÷16 = 10.6875
The most significant number is 0.6875*16 = 11
Since we can't divide anymore we have our result which is 1011
h) Following the same steps as before:
91÷3 = 30.333333333
The most significant number is 0.333333*3 = 1
30÷3 = 10
The next number is 0
10÷3 = 3.3333333333
The next number is 0.333333*3 = 1
3÷3 = 1
Since we have the final value remainder as 0 the least significant number is 1
Since we can't divide anymore we have our result which is 10101.
i) Following the same steps as before:
840÷9 = 93.333333
The most significant number is 0.33333*9 = 3
93÷9 = 10.3333333
The next number is 0.333333*9 = 3
10÷9 = 1.11111111
The next number is 0.11111111*9 = 1
Since we can't divide anymore we have our result which is 1133
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the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.
A company manufactures rubber balls, random variable X in words is diameter of the rubber ball, standard deviation is -1.5 and z-score of the x = 2 is 2.123.
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.
In probability and statistics, random variables are used to measure outcomes of a random event, and hence, can take on various values. Real numbers are often used as random variables since they must be quantifiable.
1) X denotes the diameter of the rubber ball.
So the correct option was A. (option A)
Therefore, the random variable X in words is diameter of the rubber ball.
2) For 1.5 Standard deviations left to the mean , Z score will be -1.5
option(A)
So, standard deviation to the left of the mean is -1.5.
3) [tex]Z=\frac{(x-\mu)}{\sigma}[/tex]
x=2
sigma = √2
Z = 2-(-1)/ √2
Z = 3/√2
Z = 2.123
Hence, the z-score of the x = 2 is 2.123.
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Complete question:
A company manufactures rubber balls. The mean diameter of a rubber ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X
diameter of a rubber ball
rubber balls
mean diameter of a rubber ball
12 cm
Question 2 What is the z-score of x=9, if it is 1.5 standard deviations to the left of the mean? Hint: the z-score of the mean is =0 −1.5 1.5 9 Question 3 Suppose X∼N(−1,2). What is the z-score of x=2 ? Hint: z=(x−μ)/σ 1.5 −1.5 0.2222
STUDY SKILLS 7. State ONE way in which each of the examination writing skills below could effectively assist you when writing your examinations. 7.1 Read the question 7.2 Plan the response 7.3 Answer the questions (3 x 1) (3)
Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.
These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.
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Complete question:
State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:
Read the questionPlan the responseAnswer the questionsThree dice are rolled. What is the probability of getting the sum as 13?
When three dices are rolled.
Total number of outcomes = = 216
Sum of 13 can be achieved in the following ways:
From the digits 6,4,3
So, there are 3! ways = = 6
From the digits 6,2,5
So, there are 3! ways = = 6
From the digits 5,4,4
So, there are ways = 3
From the digits 6,6,1
So, there are ways = 3
From the digits 3,5,5
So, there are ways = 3
So, total numbers whose sum is 13=
So, Probability = .
Therefore, the probability of getting sum as 21 on rolling three dice = .
(a)A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.One possible selection:Mon: Kung pao chickenTues: Beef with broccoliWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoliA different selection:Mon: Beef with broccoliTues: Kung pao chickenWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoli(b)Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
(a) There are 100,000 different ways for Fiona to select her lunches for the week.
(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.
(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:
10 × 10 × 10 × 10 × 10 = 10^5 = 100,000
(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:
100,000 × 2 = 200,000
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locate the absolute extrema of the function
on the closed interval
Answer:
To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we find the antiderivative of f(x):
F(x) = x^2 + (5/3)x + C
where C is the constant of integration.
Next, we evaluate F(5) and F(0):
F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C
F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C
Subtracting F(0) from F(5), we get:
∫[0,5] f(x) dx = F(5) - F(0)
= 25 + (25/3) + C - C
= 25 + (25/3)
= 100/3
Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.
