If one of the pedestrian death is randomly elected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated 0.6290.
Divide the applicable variety with the aid of using the whole variety. In this case, the applicable variety they may be requesting is "neither pedestrian nor driver."Neither/Total = 619/984 = 0.6290.Rounded to 4 figures that is 0.6290.This, of course, assumes that the published desk is formatted successfully and is correctly legible.Read more about pedestrian :
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The spinner below is spun twice. If the spinner lands on a border, that spin does not count and spin again. It is equally likely that the spinner will land in each of the six sectors.
For each question below, enter your response as a reduced fraction. Find the probability of spinning cyan on the first spin and red on the second spin.
Find the probability of spinning cyan on the first spin and blue on the second spin.
Find the probability of NOT spinning cyan on either spin. (Not cyan on the first spin and not cyan on the second spin.)
The probability of red on the second spin 1/12. the probability of blue on the second spin 1/18. the probability of not spinning cyan on either spin is 25/36.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
What is probability formula?The ratio of favorable outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range.
Probability = Number of Favorable Outcomes / Total Number of
we know the formula of probability;
probability=favorable outcomes/total number of outcomes
so for red:
P(red) = 3/6 = 1/2
so for blue:
P(blue) = 2/6 = 1/3
so for cyan
P(cyan) = 1/6
Now totally;
P( cyan then red) = 1/6 * 1/2 = 1/12
P(cyan then blue) = 1/6 * 1/3 = 1/18
P( no cyan on 2 spins) = (1/2+1/3)* (1/2+1/3) = 5/6 * 5/6 = 25/36
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How do you write a rule for dilation?.
The rule of dilation can be defined as to enlarge or reduce any shape or graph of any function, to create a new graph or shape.
We have to write a rule for the dilation,
A transformation is termed as an operation that moves, flips, and create a new shape.
Dilation is also a type of transformation that enlarges or reduces any shape or graph of any function, to create a new graph or shape.
The scale factor, k determines how much large or small the dilation figure will be as compared to the previous shape or figure.
So, the rule of dilation can be defined as to enlarge or reduce any shape or graph of any function, to create a new graph or shape.
Hence, the rule of dilation can be defined as to enlarge or reduce any shape or graph of any function, to create a new graph or shape.
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What is TCS enterprise agile?.
Agile promotes innovation, speeds up product delivery, and motivates workers in a world that values technology above everything else
What is enterprise ?
Despite being another word for a for-profit business or organization, the word "enterprise" is most frequently related to entrepreneurial endeavors. Those who are successful in business are frequently referred to as "enterprising." Legal businesses come in a variety of shapes and sizes, but the most popular ones in the US.
Industry goliaths can no longer win by virtue of their size and market power. Today, adapting to a constantly shifting corporate environment and quickly changing client demands requires speed and agility.
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if+there+is+a+15%+increase+in+the+aggregate+price+level,+a+consumer+who+had+been+looking+to+purchase+something+that+cost+$2,500+would+now+have+to+pay+$______+for+it.
Answer:
Step-by-step explanation:
The amount of something that needs to be bought will be $2,875.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If there is a 15% increase in the aggregate price level, a consumer who had been looking to purchase something that cost $2,500.
Let 'x' be the amount that needs to pay. Then the amount of something that needs to be bought will be given as,
x = (1 + 15%) of $2,500
x = (1 + 0.15) x $2,500
x = 1.15 x $2,500
x = $2,875
The amount of something that needs to be bought will be $2,875.
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a fair die is rolled 25 times. it landed on the number 5 eight times. what is the relative frequency of getting a 5 on the next roll?
Answer:
5/6
Step-by-step explanation:
The results of previous dice rolls don't have any effect on the result the next time the die is rolled.
The relative frequency of getting a 5 on the next roll is 5/6
How to find the relative frequency?Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency). Conditional relative frequency is relative frequency conditional to some special characteristic.
We are given that a fair die is rolled 25 times. it landed on the number 5 eight times.
We need to find the relative frequency of getting a 5 on the next roll
relative frequency = 5/6
The results of previous dice rolls that have any effect on the result the next time the die is rolled.
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What is the value of a1 of the geometric series?sigma-summation underscript n = 1 overscript infinity endscripts 12 (negative one-ninth) superscript n minus 1negative twelve-ninthsnegative one-ninths112.
the value of a1 of the geometric series sigma-summation underscript n = 1 overscript infinity endscripts 12 (negative one-ninth) superscript n minus 1negative twelve-ninthsnegative one-ninths112 is a1 = 12
Given the geometric series
Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 12 (negative one-ninth) Superscript n minus 1
From the series given, the nth term of the sequence is given as;
an = 12(1/9)^n-1
To get a1, we will substitute the value of n=1 into the nth term of Tue geometric series.
Given the nth term of the series as;
an = 12(1/9)^n-1
When n=1
a1 = 12(1/9)^1-1
a1 = 12(1/9)^0
Since anything raise to power of zero is 1, then;
(1/9)^0 = 1
a1 = 12{1}
a1 = 12
The value of a1 of the geometric series is 12.
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help pleassee!!!!!!!
Answer:
The correct answer is 5.672 x 10^3
Step-by-step explanation:
change the exponent for 3.28 x 10^2, and you get 0.328 x 10^3, and then subtract normally, which gets you 5.672 x 10^3
Carlton has a z-score of 1.74 on the achievement test. did he score higher than my score in the 98th percentile? what was carlton's score?
Cartlon's score is 4.5434.
Given that,
Carlton has a z-score 1.74 on the achievement test.
From the z-table we get the value 0.959.
We know the formula for standard deviation,
z = (x - μ) / σ
where x = score, σ = standard deviation, μ = mean
Now z-score corresponding to 98th percentile is 2.06
substituting the values in the above equations,
2.06 = (x - 0.959) / 1.74
i.e. x - 0.959 = 2.06 * 1.74
x = 3.5844 + 0.959
x = 4.5434
Therefore carlton's score is 4.5434.
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in statistical hypothesis testing, the null hypothesis and the alternative hypothesis are stated in terms of:
The correct answer is 'in statistical hypothesis testing, the null hypothesis and the alternative hypothesis are stated in terms of population parameter.
A population parameter is always used to express a statistical hypothesis: The null hypothesis is true if the test statistic's value is within the nonrejection zone.
We look for evidence supporting the null hypothesis when testing a statistical hypothesis. The null hypothesis and the alternative hypothesis are the two variants of the hypothesis that are typically used in research (called the experimental hypothesis when the method of investigation is an experiment).
According to the alternative hypothesis, a population parameter does not equal the given value. Usually, this number is zero, which is the null hypothesis value for an effect of zero.
You can reject the null hypothesis and favour the alternative hypothesis if your sample includes enough evidence to support it.
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A right triangle has legs of known lengths 2L and h. Find the length of the line segment x which is parallel to side h. Explain your reasoning.
A triangle in which one of the sides makes an angle of 90 degrees is called the right angle triangle. Three lengths of the right angle triangle are base, altitude, and hypotenuse. Various types of triangles are
(a) Right-angled triangle
(b) Isosceles triangle
(c) Equilateral triangle
The length of the line segment x equals half the height of the triangle.
What is a right triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a right triangle is a triangle in which one angle is a right angle, i.e., two sides are perpendicular. Trigonometry is based on the relationship between the sides and various angles of a right triangle.
Side an is the side adjacent to angle B that is opposed to angle A, whereas side b is the side adjacent to angle A that is opposed to angle A.
If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle, and its side lengths are referred to as a Pythagorean triple.
The triangle's designated length is L.
The triangle's designated height is h.
Take a look at the angle
The diagram is provided below.
Consider the little triangle in the diagram as
tan=x/L.
Take a look at the huge triangle; the angle is given as
tan=h/(L+L).
tanθ=h/2L
Both equations (1) and (2) can be written as
x/L=h/2L
x=h/2.
As a result, line segment x is half the height of the triangle.
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1. in semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. the etch rate is an important characteristic in this process and known to follow a normal distribution. two different etching solutions have been compared, using two random samples of 10 wafers for each solution. the observed etch rates are as follows (in mils per minute): solution 1 9.9 9.4 9.3 9.6 10.2 10.6 10.3 10.0 10.3 10.1 solution 2 10.2 10.6 10.7 10.4 10.5 10.0 10.2 10.7 10.4 10.3. (a) Do the data support the claim that the mean etch rate is the same for both solutions? In reaching your conclusions, use a fixed-level test with \alpha = 0.05α=0.05 and assume that both population variances are equal. (b) Calculate a P-value for the test in part (a). (c) Find a 95% CI on the difference in mean etch rates. (d) Construct normal probability plots for the two samples. Do these plots provide support for the assumptions of normality and equal variances? Write a practical interpretation for these plots.
P-value for the test is 0.011.
(a) We have two samples
y₁₁ = μ₁ + e₁₁
...
y₁,₁₀ = μ₁ + e₁,₁₀
y₂,₁ = μ₂ + e₂₁
...
y₂,₁₀ = μ₂ + e₂,₁₀
with unknown means μ₁ and μ₂. The total number of observation n = 20,
number of parameters p = 2.
First, we estimate the means of both samples:
û₁ = [tex]\frac{1}{10}[/tex] ∑ y₁i = 9.97, û₂ = [tex]\frac{1}{10}[/tex] ∑ y₂i = 10.4
The residual sum of squares
SSres = ∑(y₁i - û₁)^2 + ∑(y₂i - û₂)^2 = 2.081.
The unbiased variance estimate is
[tex]s^{2}[/tex] = [tex]\frac{1}{n - p}[/tex]SSres
= [tex]\frac{2.081}{18}[/tex]
[tex]s^{2}[/tex]= 0.116
In testing the null hypothesis H₀ : μ₁ = μ₂, the test statistic of the t-test is defined as
T = |û₁ - û₂|/([tex]\sqrt{s^{2}(\frac{1}{10}+\frac{1}{10} ) }[/tex])
T= 2.83.
Since t18(0.05/2) = 2.1
the hypothesis H₀ is rejected, at the significance level 5%. In other words, under the standard assumptions, the data do not support the claim that the mean each rate is the same for both solutions, at the level of significance 5%.
(b)
p = P(|T18| > T)
= 2P(T18 > T)
p = 0.011.
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7
12
+
11
20. Y’all pls help me I got no cle
The solution of the expression will be;
⇒ - 1/30
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
The expression is,
⇒ - 7/12 + 11/20
Now,
Simplify the expression as;
⇒ - 7/12 + 11/20
LCM of [12, 20] = 60
⇒ - 35/60 + 33/60
⇒ (- 35 + 33) / 60
⇒ - 2/60
⇒ - 1/30
Thus, The solution of the expression will be;
⇒ - 1/30
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Solve the equation 2cos x+ √2=0 for solutions of x in the interval [0°, 360°).
The solutions of x in the interval [0°, 360°) are 3[tex]\pi[/tex]/4 and 5[tex]\pi[/tex]/4 respectively.
What is a quadrant?
The quadrant is the area that is bounded by the point where the X and Y axes connect.
A plane is split into four sections in the cartesian system, the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.
Given, 2cos x + √2 = 0
or, 2cos x = -√2
or, cos x = -√2/2 = -1/√2 = - cos ([tex]\pi /4[/tex] )
As the given cos(x) is negative, then it must lie in quadrants II and III respectively for the given interval [0°, 360°).
Then, cos x = cos ([tex]\pi[/tex] - [tex]\frac{\pi}{4}[/tex]) and, cos x = cos ([tex]\pi +\frac{\pi }{4}[/tex])
or, x = 3[tex]\pi[/tex]/4 or, x = 5[tex]\pi[/tex]/4
Hence, the required solutions of x are 3[tex]\pi[/tex]/4 and 5[tex]\pi[/tex]/4.
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Find the dimensions of a rectangle with perimeter 72 m whose area is as large as possible. Step 1 Let / and w represent the length and the width of the rectangle, measured in m. Let A represent the area of the rectangle, measured in m2. Writing an equation for A in terms of land w gives us the following. m2 A= in terms of/ and w Let P represent the perimeter of the rectangle, measured in m. Writing an equation for gives us the following. P= m
By using the concept of maxima, it can be calculated that
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
What is maxima of a function?
Maxima of a function gives the maximum value of the function in a given interval or in the whole domain.
Let the length of the rectangle be l m and width of the rectangle be w m
Perimeter (P) = 2(l + w)
By the problem,
2(l + w) = 72
l + w = [tex]\frac{72}{2}[/tex]
l + w = 36
w = 36 - l
Area (A) = l [tex]\times[/tex] w
A = l [tex]\times[/tex] (36 - l) = [tex]36l - l^2[/tex]
Differentiation with A with respect to l
[tex]\frac{dA}{dl} = 36 - 2l[/tex]
For maximum area,
[tex]\frac{dA}{dl} = 0[/tex]
36 - 2l = 0
2l = 36
l = [tex]\frac{36}{2}[/tex]
l = 18 m
[tex]\frac{d^2A}{dl^2} = -2 < 0[/tex]
Hence area is maximum
w = 36 - 18 = 18 m
Length of the rectangle of perimeter 72 m with maximum area is 18 m
Breadth of the rectangle of perimeter 72 m with maximum area is 18 m
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Can someone help me on this question?
I don't know the answer but I believe it could be the 3rd one
Which expression is equivalent to 3m+m?
Four equivalent forms of a quadratic function are given. which form displays the y-intercept of the function?
The quadratic function f(x) = 3x^2 + 6x – 144 displays the y-intercept of the function.
In the given question, four equivalent forms of a quadratic function are given.
We have to choose which form displays the y-intercept of the function.
The given quadratic functions are:
f(x) = 3(x^2 + 2x - 48)
f(x) = 3(x + 1)^2 - 147
f(x) = 3x^2 + 6x – 144
f(x) = 3(X + 8)(x-6)
As we know that in y intercept form x=0.
A quadratic equation's Y intercept is the location where the graph's Y-axis is broken. This implies that the x axis's coordinates must be zero.
Put x = 0 in the equation to determine the Y intercept in a quadratic equation. You will also receive the Y interception.
Since we have to find the y intercept in the given form so the function
f(x) = 3x^2 + 6x – 144 given in a standard form and y intercept is clearly seen in this function.
So, the function f(x) = 3x^2 + 6x – 144 displays the y-intercept of the function.
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The right question is
Four equivalent forms of a quadratic function are given. Which form displays the y-intercept of the function?
f(x) = 3(x2 + 2x - 48)
f(x) = 3(x + 1)2 - 147
f(x) = 3x2 + 6x – 144
f(x) = 3(X + 8)(x-6)
the residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was to . if there were no votes, what was the total number of votes?
The total number of no votes are 4422.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given: The ratio of yes votes to no votes is 5 to 6 i.e.
yes votes /no votes = 5/6
It means there are total 11 votes ( 5 votes for yes and 6 votes for no)
which gives
no votes/total votes= 6/11---(i)
But in the given question total votes are 8107,
so let us consider there are x votes for no which implies
no votes/total votes= x/8107
From (i), we have
x/8107 = 6/11
⇒ x = 6*8107/11 = 4422.
Then the total number of no votes is 4422.
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NOTE: The question given in the portal is incomplete. Here is the complete question.
Question: The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 8107 total votes, how many no votes were there?
What is the equation of a line that is parallel to 2x 3y = 3 and passes through the point (3, −4)? enter your answer in the box.
The correct answer is the equation of the line is y = [tex]-\frac{2}{3} x - 2[/tex]
Given the equation of the parallel line is 2x + 3y = 3
and the required line passes through the point (3, -4) where x is 3 and y is -4
We can write the given equation as:
⇒ 3y = 3 - 2x
Dividing both sides by 3
[tex]y = 1 - \frac{2x}{3}[/tex]
On comparing this equation with y= mx+b, thus m = [tex]-\frac{2}{3}[/tex] and the slopes of parallel lines are always equal.
Using the point slope form, we will derive the equation of line
⇒ [tex]y-y_1 =m ( x- x_1)[/tex]
⇒ [tex]y- (-4) = -\frac{2}{3} (x-3)[/tex]
⇒ [tex]y+4= -\frac{2}{3} (x) - \frac{2}{3} (-3)[/tex]
⇒ [tex]y = -\frac{2}{3} (x) +2-4[/tex]
⇒ [tex]y = -\frac{2}{3} (x) - 2[/tex]
Hence, the equation of the required line is [tex]y = -\frac{2}{3} (x) - 2[/tex]
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the radius of a sphere is decreasing at a constant rate of 5 centimeters per minute. at the instant when the volume of the sphere is 16111611 cubic centimeters, what is the rate of change of the volume? the volume of a sphere can be found with the equation
The rate of change of the volume of sphere when is decreasing at a constant rate is found as 3319.16 cm³/min.
Define the term rate of change?An indicator of how some quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.For the stated question-
A sphere's radius is shrinking at a steady rate of 5 centimeters per minute.The sphere's volume is 1611 cubic centimeters at that precise moment,Thus, the volume of sphere is found by the equation.
Volume of sphere V = 4/3 πr³
V = 1611 cm³.
1611 = 4/3 πr³
On solving,
r = 7.27 cm
Rate change of the volume;
dV/dt = 4/3 πr² × 3
dV/dt = 4 πr²
Put r = 7.27 cm and π = 3.14
dV/dt = 4 x 3.14 x 7.27²
dV/dt = 3319.16 cm³/min.
Thus, the rate of change of the volume of sphere when is decreasing at a constant rate is found as 3319.16 cm³/min.
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to qualify for a medical study, an applicant must have a systolic blood pressure in the of the middle range. if the systolic blood pressure is normally distributed with a mean of and a standard deviation of , find the upper and lower limits of blood pressure a person must have to qualify for the study.
The upper limit of blood pressure is 123.4.
The lower limit of blood pressure is 116.6..
The applicant's blood pressure limit does not meet the standards limit of blood pressure to qualify for study.
we have given that,
mean , μ = 120
standard deviation , σ = 4
The z - distribution of the 60% is,
P( -z < Z < z ) = 0.60
P( Z < z ) - P( Z < -z ) = 0.60
2× P(Z < z ) - 1 = 0.60
2× P(Z < z ) = 1 + 0.60
P( Z < z ) = 1.60 / 2
P( Z < z ) = 0.80
P( Z < -0.84) = 0.80
z = -0.84 and z = 0.84
let X be the required mean of sample .
Using z - score formula,
X = (z × σ )+ μ
= -0.84 × 4 + 120
= 116.6
and
X = z × σ + μ
= 0.84 × 4 + 120
= 123.4
Hence , Lower blood pressure limit = 116.6
Upper blood pressure limit = 123.4
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Complete question:
To qualify for a medical study, an applicant must have a systolic blood pressure in the 60% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, find the upper and lower limits of blood pressure a person must have to qualify for the study. Round final answers to 1 decimal place and intermediate-value calculations to 2 decimal places. Applicants must have a lower blood pressure limit of 118.48 and an upper blood pressure limit of 124.16 to qualify for the study.
use dalton's law to calculate the partial pressure (in torr) of hydrogen gas in the gas-collecting tube. blank1 - numeric answer type your answer here torr (or mmhg)
The pressure is assessed through the ideal gas equation and Dalton's law
Partial Pressure of hydrogen gas in the gas collecting tube can be calculated as:
According to Dalton's law, the total pressure of the system will be the sum of partial pressure of all gases
In the system, the pressure is exerted by the water and gas.
Total pressure = P(water) + P(Hydrogen)
P(hydrogen) = 746 mm Hg (given) = 19.8 mm Hg +
P(hydrohen) = = 746 mm Hg - 19.8 mm Hg
= 726.2 mm Hg
So, the partial pressure of Hydrogen was found to be 726.2 mm Hg.
To calculate the volume of hydrogen at STP, ideal gas equation is used.
For this, we calculate the moles of Hydrogen in given conditions:
Pressure = 726.2 mm Hg
= 726.2/760
= 0.955 atm
Therefore, The pressure is assessed through the ideal gas equation and Dalton's law
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surface area of a cube if the sides are 0.7
Answer:
[tex]SA = 2.94 \, \textrm{units}^2[/tex]
Step-by-step explanation:
The surface area of a regular 3D figure can be represented as:
[tex]SA = A_{\textrm{\,1 side}} \cdot (\# \textrm{ of sides})[/tex].
Therefore, the surface area of a cube is:
[tex]SA = s^2 \cdot 6[/tex]
where [tex]s[/tex] is the length of a side.
To solve this problem, simply input the given side length into the above formula:
[tex]SA = 0.7^2 \cdot 6[/tex]
and simplify.
[tex]SA = 0.49 \cdot 6[/tex]
[tex]SA = 2.94 \, \textrm{units}^2[/tex]
Three friends split the cost of living together evenly. Their rent is $690, and their other expenses total $859. 32. How much does each person pay?.
Each person will pay $516.44.
What does splitting the cost means?To split an expense means to divide it into equal parts among the data given.
Over here we have, three friends so we will split the amount among them.
Here, sharing the cost of living means first calculating their total expenses (rent and other costs), which must then be divided among them.
They spend $859.32 on additional expenses in addition to their $690 rent payment.
Their total expenses are rent and other costs.
$690 + $859.32 = $1549.32.
We must now divide the money among the three friends 1554.32/3 =$516.44.
Therefore each individual will pay $516.44.
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Exercise 8-9 Algo A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 16 houses that sold in their neighborhood took an average time of 250 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 55 days. [You may find it useful to reference the z table.) a. What assumption regarding the population is necessary for making an interval estimate for the population mean? O Assume that the population has a normal distribution Assume that the central limit theorem applies b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "?' value to 3 decimal places and final answers to 2 decimal places.) Confidence interval
Making an interval estimate for the population mean requires making the following assumptions about the population:
a. The population is thought to have a normal distribution.
b. The central limit theorem is presumptively true.
Given,
Making an interval estimate for the population mean requires making the following assumptions about the population:
a. The population is thought to have a normal distribution.
b. The central limit theorem is presumptively true.
The distribution of a variable's values is described by a normal distribution. There are 50% of the data to the left and 50% to the right of the mean in this probability distribution, which is symmetrical about the mean. The majority of the data are centered around the mean, meaning that they are more likely to occur or be located close to the mean than distant from it. A bell curve will represent the normal distribution's graph form. Mean = mode = median describes a normal distribution.
According to the Central Limit Theorem, when a variable does not follow a normal distribution, repeated random samples from the population will result in sample means that are normally distributed, regardless of the underlying distribution of the sample. This indicates that as the sample size increases, the sampling distribution of the sample means moves closer to a normal distribution.
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assuming no one is cheating and the coin is fair, if a customer plays twice, what is the chance they make money?
Answer:
Step-by-step explanation:
(1/2)(1/2)=1/4
b) In a different Fibonacci sequence the fourth term is 30 and the fifth term is 49.
Write down the first term in this sequence.
c) The second and third terms in the following Fibonacci sequence are x and y.
Write down algebraic expressions for the first, fourth and fifth terms.
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The given Fibonacci sequence ,
b) First term of the Fibonacci sequence is 8.
c) First term = y-x.
Fourth term = x+y
Fifth term = y+30.
What is Fibonacci Sequence?
A series in which each number is the sum of the two numbers before it is known as the Fibonacci Sequence. We must specify values for the first two terms in order to complete the Fibonacci Sequence. In the Fibanocci sequence we can find next term by adding previous terms.
Here the given Fourth term = 30 and Fifth term = 49.
Here second and third terms are x and y. Let us take first term as a.
We know that the Fibonacci sequence is sum of previous terms.
The sequence are,
=> a , x , y , 30 ,49 ,...
Here Fourth term = 30
=> second term + third term = 30
=> x+y = 30----->1
Now the fifth term is third term + fourth term = 49
=> y+30 =49
=> y =19.
Put y=19 into 1 then,
=> x+19=30
=> x = 30-19 =11
Now third term is first term+second term = third term
=> a+x =y
=> a+11=19
=> a =19-11 =8.
b) First term of the Fibonacci sequence is 8.
c) Third term = first term+second term
=> y = first term +x
=> First term = y-x.
Fourth term = Second term+third term
=>Fourth term = x+y
Fifth term = third term+fourth term
=> Fifth term = y+30.
Therefore the given Fibonacci sequence ,
b) First term of the Fibonacci sequence is 8.
c) First term = y-x.
Fourth term = x+y
Fifth term = y+30.
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you are asked to help with the radiodating of a plant based sample excavated from an archaeological site. the rate of 14c decay in the sample is 73.0% of the 14c decay rate in a living plant. what is the estimated age of the archaeological sample? (the half-life for 14c is 5730 years.)
The estimated age of the archaeological sample as calculated from the given data is = 2622.58333 years
Half life given is 5730
t₆.₅ = Ln2/k
k= ln 2/ 5730
The rate constant ,
k = 0.00012 year⁻¹
Given that 73 % of the 14C remains
then |A1|/|A2| = 0.73
As we know ,
|A1|/|A2| = e ⁻₍kt₎
Hence, on solving the equation we get ,
ln(0.73)= -0.00012t
t = -0.31471/ -0.00012
= 2622.58333 years
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay.
For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.
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What are the coefficients for the binomial expansion of (a + b)3? 1, 4, 6, 4, 1 1, 1 1, 2, 1 1, 3, 3, 1.
(A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.
What are coefficients?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.
It is typically a number, but it can also be any expression.
They may also be referred to as parameters if the coefficients are variables in and of themselves.
A coefficient is, in other words, the numerical factor of a term that contains both constants and variables.
For instance, the coefficient in the expression 2x is 2.
So, we have: (a + b)3
Since we have nothing before (a + b)3.
Then the coefficient will be 1 here.
If we have 3 after (a + b) then the coefficient will be 3.
Therefore, (A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.
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Correct question:
What are the coefficients for the binomial expansion of (a + b)3?
a. 1, 4, 6, 4, 1
b. 1,1
c. 1, 2,1
d. 1,3,3, 1
what is the alternative hypothesis if we want to test the hypothesis that the mean score on campus 1 is higher than on campus 2?
μ1 <= μ2,
mean score on campus 1 is higher than on campus 2
What is alternative hypothesis ?
There is also a competing theory put forth by the researcher, according to which test results are unrelated and the advanced learning program has minimal bearing on students' academic performance. Because the researcher wants to know if the scores are greater or lower than the state average, this is an illustration of a two-sided hypothesis.
μ1 <= μ2,
mean score on campus 1 is higher than on campus 2.
Because the researcher wants to know if the scores are greater or lower than the state average, this is an illustration of a two-sided hypothesis.
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