The value of standard deviation of the stock returns is 10.246%.
What is standard deviation?The variance or dispersion of a group of data points is measured by standard deviation. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined. In statistics, the term "standard deviation" is used to characterise the distribution of a data collection and to estimate the probability of certain outcomes or events.
The standard deviation is determined using the formula:
√(V).
The mean of the given data is:
(−12 + 10 + 5 − 7 + 3) / 5 = −0.2%
Now, the variance is:
Variance = [ (−12 − (−0.2))² + (10 − (−0.2))² + (5 − (−0.2))² + (−7 − (−0.2))² + (3 − (−0.2))² ] / 5
Variance = 104.96
Now, for standard deviation:
Standard deviation = √(104.96) = 10.246%
Hence, the value of standard deviation of the stock returns is 10.246%.
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The cost white in dollars for X pounds of deli meat is represented by the equation Y equals 3.5 X graph the equation and interpret the slope
The graph is of the given equation is represented in the figure below.
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.
Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:
[tex]y = 3.5x[/tex]
The graph is of that linear equation as plotted below diagram.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.
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The graph is of the given equation is represented in the figure below linear line: Y = 3.5x
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude indicates that the price per pound of deli meat has changed by 3.5 units.
Given linear equation represents the cost measured in dollars, as a function of the amount of deli meat, measured in pounds:
Linear line: Y = 3.5x
The graph is of that linear equation as plotted below diagram.
By dividing the price change by the fluctuation in the amount of deli meat, one may calculate the slope. The magnitude denotes a change in the price per pound of deli meat of 3.5 units.
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a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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What are the coordinates of point G on the coordinate grid below?
A
(-4,3)
(4,-3)
-2
4
2
O
-2
4
B
AY
D
2
(4,3)
(-4,-3)
4
G
XA
Answer:
The answer is G = (4,3)
Step-by-step explanation:
G = (4,3)
The relative housing cost for a US city is defined to be the ratio nationalaveragehousingcost
averagehousingcostforthecity
, expressed as a percent.
The scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005. The line of best fit is also shown and has equation y=0.0125x+61. Which of the following best explains how the number 61 in the equation relates to the scatterplot?
In 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.
We know that the relative housing cost for a US city is defined to be the ratio average housing cost for the city /national average housing cost, expressed as a percent also the scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005, therefore,
the equation is y = 0.0125x + 61
Therefore, with this we know that in 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.
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PLS HELP FAST 20 POINTS + BRAINLIEST
Answer:
£22
Step-by-step explanation:
50% of 88=88/100 ×50=44
44÷2=25%=22
75% of £88 is deducted, so that 88-66=£22
Don't forget my Brainliesta triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square
The cοst οf painting the triangle bοrder at the given rate is Rs. [tex]108\sqrt{(2)[/tex].
What is a triangle?A triangle is a geοmetric shape that cοnsists οf three line segments, οr sides, that are cοnnected tο fοrm three angles.
Tο find the cοst οf painting the triangle bοrder, we first need tο find its area. Let's call the third side οf the triangle "x".
We knοw that the perimeter οf the triangle is 24cm, sο we can write an equatiοn:
6cm + 8cm + x = 24cm
Simplifying this, we get:
x = 10cm
Nοw we can use Herοn's fοrmula tο find the area οf the triangle:
s = (6cm + 8cm + 10cm)/2 = 12cm
Area [tex]= \sqrt{(s(s-6cm)(s-8cm)(s-10cm))[/tex]
[tex]= \sqrt{(12cm6cm4cm*2cm)[/tex]
[tex]= 2\sqrt{(72cm^2)[/tex]
[tex]= 12\sqrt{(2) cm^2[/tex]
Finally, we can calculate the cοst οf painting the bοrder at a rate οf Rs. 9 per square cm:
Cοst = (Area) x (Rate)
[tex]= (12\sqrt{(2)} cm^2) x (Rs. 9/cm^2)[/tex]
[tex]= Rs. 108\sqrt{(2)[/tex]
Therefοre, the cοst οf painting the triangle bοrder at the given rate is= [tex]Rs. 108\sqrt{(2)[/tex]
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2. problem 4.3.4 for a constant parameter , a rayleigh random variable x has pdf what is the cdf of x?
The cumulative distribution function (CDF) for given random variable fx(x) is given by F(x) = 1 - e^[(-a²)(x²/2)] x > 0,
F(x) = 0 x ≤ 0.
The cumulative distribution function (CDF) F(x) for a Rayleigh random variable X is defined as,
F(x) = P(X ≤ x)
To find the CDF of X, we integrate the PDF of X over the interval [0, x],
F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx
Using the substitution u = (-a²x²/2),
Simplify the integral as follows,
F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx
= ∫₀^((-a²x²)/2) -e^u du (where u = (-a²x²/2) and x = √(2u/a²))
= [e^u]₀^((-a²x²)/2)
= 1 - e^[(-a²)(x²/2)]
Therefore, the CDF of X for the Rayleigh random variable X has PDF fx (x) is equal to,
F(x) = 1 - e^[(-a²)(x²/2)] x > 0,
F(x) = 0 x ≤ 0.
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The above question is incomplete, the complete question is:
For a constant parameter a > 0, a Rayleigh random variable X has PDF
fx (x) = a²xe^[(-a²)(x²/2)] x > 0
0 otherwise.
What is the CDF of X?
When an octave is divided into twelve equal steps, a chromatic scale results. The ratios between sucessive notes is
constant.
IC C# D D# E F F# G G# А A# B с
261.6 277.2
293.6
329.6 349.2 370.0 392.0
1440 466.1 493.8 523.2
Determine the missing frequency for G# and D# using the ratio 1.0595. Round to the nearest tenth. What is the ratio
of frequencies between G# and D#? Would these two notes be consonant or dissonant?
4
1.338
consonant
31
a.
b.
3
1.338
41
consonant
c.
14
1.338
4
dissonant
d.
1.33
4
3
dissonant
The ratio of frequencies between G# and D# is: G# / D# = 415.3 / 293.7 ≈ 1.414
To find the missing frequencies for G# and D# using the ratio 1.0595, we need to multiply the frequency of the previous note by 1.0595. Starting from A440, we can use this ratio to calculate the frequencies of G# and D#:
G#: 440 x 1.0595^8 ≈ 830.6 Hz
D#: 440 x 1.0595^6 ≈ 622.3 Hz
The ratio of frequencies between G# and D# is:
830.6 / 622.3 ≈ 1.334
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Solve the following problems.
Given: AABC, DE AC,
BD DC, mZ1=m22,
mZBDC= 100°
Find: m< A, m< b , m
The value of the angles in the triangle are:
∠A = 60°, ∠B = 80° and ∠C = 40°
How to find the value of m∠A, m∠B, m∠C in the triangle?
We are given that BD = DC
Thus, ∠DBC = ∠BCD ---- 1 (angle in isosceles triangle)
We also have ∠BDC = 100°
In ΔBDC
∠BDC + ∠DBC + ∠BCD = 180° (sum of angles of triangle is 180°)
Using 1:
∠BDC + 2∠DBC = 180°
100° + 2∠DBC = 180°
2∠DBC = 180 - 100
2∠DBC = 80
∠DBC = 80/2
∠DBC = 40°
∠DBC = ∠BCD = ∠2 = 40°
Thus, ∠C = 40°
We are given that m∠1 = m∠2
Thus, ∠1 = ∠2 = 40°
Now, ∠BDC + ∠BDA = 180° (Linear pair)
100° + ∠BDA = 180°
∠BDA = 180 - 100
∠BDA = 80°
In ΔABD
∠ABD + ∠BDA + ∠BAD = 180° (sum of angles of triangle is 180°)
∠1 + ∠BDA + ∠BAD = 180°
40° + 80° + ∠BAD = 180°
120° + ∠BAD = 180°
∠BAD = 60°
So, ∠A = 60°
∠B = ∠1 + ∠2 = 40° + 40° = 80°
Therefore, ∠A = 60°, ∠B = 80° and ∠C = 40°
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Complete Question
m∠1=m∠2
D∈
AC
, BD = DC
m∠BDC = 100°
Find: m∠A, m∠B, m∠C
under the normal distribution, if the mean of the distribution of raw scores is equal to 100, then its equivalent z-score is equal to
The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.
Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.
The z-score formula is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.
Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.
If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:
z = (115 - 100) / 15 = 1
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Write a quadratic inequality represented by the graph.
Using the concept of parabola, the quadratic inequality represented by the graph can be written as:
y = x² -2x +2.
Define parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.
The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.
The general equation for a parabola is given as:
y = a(x-h) ² + k
Now here we have:
(x,y) = (2,5)
(h,k) = (1,1)
Putting these values in the equation,
5 = a (2-1) ² + 1
a = 5-1
=4
Substituting the values:
y = (x-1) + 1
y = x² -2x +2
Therefore, the quadratic inequality can be written as: y = x² -2x +2.
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Find the 6th term of the geometric sequence described below.
m₁ = -3(-5)-1
Show your work here
Hint: To add an exponent (z"), type "exponent" or press "A"
Answer:
m₆ = 9375
Step-by-step explanation:
Given sequence is
[tex]m,_i = -3(-5)^{i - 1}[/tex]
To find the 6th term, all you have to do is substitute i = 6 and compute
For i = 6 we get
[tex]m_6 = -3(-5)^{6 - 1}\\= -3(-5)^5\\\\= -3(-3125) \\\\= 9375[/tex]
A negative number raised to an odd number is negative that is why (-5)⁵ is negative
Given the triangle below, what is mA, rounded to the nearest tenth? B 12 Triangle not drawn to scale A. 60.4° B. 2.2° 10 O C. 58.2° OD. 55.8° C SUBMIT
Answer:
C
Step-by-step explanation:
find the equation of the line with slope 2 that goes through the point (6,1). answer using slope-intercept form.
The equation of the line with slope 2 that goes through the point (6,1) in slope-intercept form is y = 2x - 11. This means that the y-intercept of the line is -11, and the slope of the line is 2, which means that for every increase of 1 in x, the line will increase by 2 in y.
To find the equation of a line with a given slope and a point on the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point on the line.
In this case, the slope is given as 2 and the point (6,1) is on the line. Plugging these values into the equation, we get:
y - 1 = 2(x - 6)
Expanding the right side, we get:
y - 1 = 2x - 12
Adding 1 to both sides, we get:
y = 2x - 11
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mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each
Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".
Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".
Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".
Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".
Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.
Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".
Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".
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I will mark you brainiest!
What is the length of BC?
A) 1.7
B) 2.1
C) 3.8
D) 4.6
Answer:
B. 2.1
Step-by-step explanation:
If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.
For △ACD, AC is hypotenuse so sinA = CD/AC
=> CD = 5 x sin(20) = 5 x 0.342 = 1.71
then we have AB = AD + BD
Pythagorean theorem: c^2 = a^2 + b^2
for △ACD, 5^2 = 1.71^2 + AD^2
AD^2 = 5^2 - 1.71^2 = 22.0759
AD = 4.70
BD = AB - AD = 6 - 4.70 = 1.30
for △BCD, BC is hypotenuse
BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61
BC = √4.61 = 2.1
the solution set is
5r+20/10=3r-6/3
Answer:
r = -2
Step-by-step explanation:
5r + 20/10 = 3r -6/3
5r + 2 = 3r - 2
2r + 2 = -2
2r = -4
r = -2
Answer: r = -2
Step-by-step explanati
What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}
Answer:
[tex]b) \quad(-1,0,2)[/tex]
Step-by-step explanation:
The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation
Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value
Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D:please !!!!
If the top of Bria's bookcase has a length-to-width ratio of 3:1, the width of the top should be about 10 inches to provide an area of 300 square inches for her soap carving collection.
How to find the dimension of the top of the bookcaseThe top of the bookcase is a rectangle, the area of the top can be expressed as the product of its length and width:
Area of the top = length × width
Area of the top = 300 square inches
length × width = 300 square inches
width = 300 square inches / length
Assuming that the top of the bookcase is with a length-to-width ratio of
3 : 1
length = 3 × width
substituting the value gives
width = 300 / (3 × width)
Simplifying, we have:
width² = 100 square inches (the polynomial)
Taking the square root of both sides, we get:
width = √100 ≈ 10 inches
Then the length will be = 30 inches
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A pollster recorded the size of households in his
area. The table below shows the distribution for
820 families. How many of the 820 families has at
least 3 people in the household?
Number of people in
a household
1
2
3
4
5
6 or more
% of Households
27%
33%
24%
10%
4%
2%
✩
Step 1: Calculate the number of families with 1 person in the household by multiplying the percentage (27%) and the total number of families (820) - 27% x 820 = 220.4.
Step 2: Calculate the number of families with 2 people in the household by multiplying the percentage (33%) and the total number of families (820) - 33% x 820 = 271.6.
Step 3: Calculate the number of families with 3 people in the household by multiplying the percentage (24%) and the total number of families (820) - 24% x 820 = 196.8.
Step 4: Calculate the number of families with 4 people in the household by multiplying the percentage (10%) and the total number of families (820) - 10% x 820 = 82.
Step 5: Calculate the number of families with 5 people in the household by multiplying the percentage (4%) and the total number of families (820) - 4% x 820 = 32.8.
Step 6: Calculate the number of families with 6 or more people in the household by multiplying the percentage (2%) and the total number of families (820) - 2% x 820 = 16.4.
Step 7: Add the numbers calculated in Steps 1 - 6 to get the total number of families with at least 3 people in the household - 220.4 + 271.6 + 196.8
Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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Mrs Devi bought banana cakes and marble cakes for a party. She spent $112 on the cakes. Each
piece of banana cakes cost $2.50 and the cost of each piece of marble cake was 7/5 the cost of
each piece of banana cake. 30% of what she bought were marble cakes. How many pieces of
cake did Mrs Devi buy?
In linear equation, 28 pieces of cake did Mrs Devi buy.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Cost of M cake = $3.5
For every 3 M cakes she bought 7 B cakes.
Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28
She bought $112 / $28 = 4 units of cakes.
Which means 12 M cakes and 28 B cakes.
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Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.
The likelihood that one or more of the dice will land on an even number is 1296.
How does probability work?The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.
According to the given information:Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.
For 2 of the same: 5×5×642) =900
For 3 of the same: 5×643) =120
For 4 of the same: 644) =6
Combined: 900+120+6=1026
Total possibilities: 64=1296
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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.
The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Therefore, the probability that at least one of the dice lands on an even number is:
1 - 1/16 = 15/16
So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
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Find the 66th derivative of the function f(x) = 4 sin (x)…..
In response to the stated question, we may state that As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
Using the chain rule and the derivative of the sine function repeatedly yields the 66th derivative of the function [tex]f(x) = 4 sin (x).[/tex]
The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x), and this pattern repeats itself every two derivatives.
As a result, the first derivative of f(x) is:
[tex]f'(x) = 4 cos (x)[/tex]
The second derivative is as follows:
[tex]f"(x) = -4 sin (x)[/tex]
The third derivative is as follows:
[tex]f"'(x) = -4 cos (x)[/tex]
The fourth derivative is as follows:
[tex]f""(x) = 4 sin (x)[/tex]
And so forth.
[tex]f^{(66)(x)} = 4 sin (x)[/tex]
Because the pattern repeats every four derivatives, the 66th derivative is the same as the second, sixth, tenth, fourteenth, and so on.
As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
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The linear sf of two similar shapes is 2:5 if the area of the similar shapes is 78cm determine the area of the bigger solid
The area of the bigger solid is 67.24 cm².
How to calculate the area of solid ?Assume the smaller shape has a length of 2x and a width of 2y. The larger shape would then have 5x length and 5y width.
Because the area of a rectangle is the product of its length and width, the area of the smaller shape is:
Area of smaller shape = 2x * 2y = 4xy
We know that the similar shapes have an area of 78 cm2. As a result, we can write:
4xy + larger area = 78
(larger shape area) / (smaller shape area) = (linear scale factor)²
Substituting the values from the problem yields:
(larger shape area) / (4xy) = (5/2)2 = 25/4
When we multiply both sides by 4xy, we get:
larger shape area = (25/4) * 4xy = 25xy
Now we can plug the expression we discovered for the area of the smaller shape into the equation we found earlier:
4xy + 25xy = 78
29xy = 78
xy = 78/29
Substituting this xy value into the expression we discovered for the area of the larger shape yields:
larger shape area = 25xy = 25 * (78/29) = 67.24 cm2 (rounded to two decimal places)
As a result, the larger shape has an area of approximately 67.24 cm2.
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what are the transformations of the following 1) f(x)=3x2^x+4-1
2) f(x)=-1/2x5^x-2+6
3) g(x)=1/5log(x+5)+3
4) g(x)=-4log(x)-2
1. The functiοn [tex]f(x) = 3x2^x+4-1[/tex]undergοes the fοllοwing transfοrmatiοns
A vertical translatiοn dοwnward by 1 unit (the [tex]"-1[/tex]" at the end)
An upward vertical stretch by a factοr οf 3 (the "3" cοefficient in frοnt)
An expοnential grοwth with base 2 (the expοnent "x" in the term [tex]"2^x"[/tex])
A hοrizοntal shift tο the left by 4 units (the "-4" in the expοnent οf [tex]"2^x"[/tex])
2. The functiοn [tex]f(x) = -1/2x5^x-2+6[/tex] undergοes the fοllοwing transfοrmatiοns:
A vertical translatiοn upward by 6 units (the "+6" at the end)An upward vertical cοmpressiοn by a factοr οf 1/2 (the [tex]"-1/2"[/tex]cοefficient in frοnt)An expοnential grοwth with base 5 (the expοnent "x" in the term [tex]"5^x[/tex]")A hοrizοntal shift tο the left by 2 units (the[tex]"-2"[/tex] in the expοnent οf [tex]"5^x[/tex]")3. The functiοn [tex]g(x) = 1/5log(x+5)+3[/tex] undergοes the fοllοwing transfοrmatiοns:
A vertical translatiοn upward by 3 units (the "+3" at the end)A hοrizοntal shift tο the left by 5 units (the "+5" inside the lοgarithm)A vertical stretch by a factοr οf 1/5 (the [tex]"1/5"[/tex] cοefficient in frοnt)4. The functiοn [tex]g(x) = -4log(x)-2[/tex] undergοes the fοllοwing transfοrmatiοns:
A vertical translatiοn dοwnward by 2 units (the [tex]"-2"[/tex] at the end)A vertical cοmpressiοn by a factοr οf 4 (the[tex]"-4"[/tex] cοefficient in frοnt)A hοrizοntal shift tο the right (there is nο explicit shift, but the dοmain οf the functiοn is restricted tο[tex]x > 0[/tex], which means the graph is shifted tο the right οf the y-axis)
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PLEASE HELPPP ME MATH
The coordinates of the image of point D that ensures that the triangles are congruent is (-2, 2)
How to determine the coordinates of point DGiven the triangle ABC and the incomplete triangle DEF
From the triangle transformation of points B and C, we can see that
The points of the triangle ABC are translated to the left by 6 units and downward by 4 units
Mathematically, this can be represented as
(x, y) = (x - 6, y - 4)
Given that
A = (4, 6)
So, we have
D = (4 - 6, 6 - 4)
Evaluate the difference
D = (-2, 2)
Hence, the position is (-2, 2)
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place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.
A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.
So, as per the given option, the correct sequence should be, B, A, E, C, D, F.
We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.
When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.
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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
A. Select the level of significance
B. setup null and alternative hypothesis
C. Establish the decision rule
D. performance computation
E. select the test statistics
F. Draw conclusions
At a community college, a survey was taken to determine where students study on campus. Of the 250 students surveyed, it was determined that
170 studied in the library
135 studied in the cafeteria
76 studied in both the library and the cafeteria
How many studied in library or cafeteria (including both)?
Answer:
Step-by-step explanation:
To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.
So, the number of students who studied in library or cafeteria is:
170 + 135 - 76 = 229
Therefore, 229 students studied in the library or cafeteria (including both).