The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
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Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.
The rate at which a rumor spreads through a town of population N can be modeled by the equation dt/dx = kx(N−x) where k is a constant and x is the number of people who have heard the rumor. (a) If two people start a rumor at time t=0 in a town of 1000 people, find x as a function of t given k=1/250. (b) When will half the population have heard the rumor?
(a) The function x as a function of t is t = 250ln(499x/998)
(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.
(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate
dt/dx = kx(N−x)
dt/(N-x) = kx dx
Integrating both sides, we get
t = -1/k × ln(N-x) - 1/k × ln(x) + C
where C is the constant of integration.
To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:
0 = -1/k * ln(N-2) - 1/k * ln(2) + C
C = 1/k * ln(N-2) + 1/k * ln(2)
Substituting C back into the equation, we get:
t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)
Simplifying, we get
t = 1/k * [ln((N-2)x/(2(N-x)))]
Substituting k=1/250 and N=1000, we get:
t = 250ln(499x/998)
(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get
t = 250ln(499(500)/998) = 250ln(249/499)
t ≈ 109.86
Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.
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Jenny took the car, the bus, and the train to get home in time.
What form of punctuation is missing?
O A. No punctuation is missing.
OB.
A period
OC.
A comma
OD. A semicolon
Last three times I have tried to take a picture of my question. Nothing comes up that resembles any of it. I don’t know what’s wrong with this app but it’s not helping.
According to the question. A. No punctuation is missing.
What is punctuation ?Punctuation is the use of symbols to indicate the structure and organization of written language. It is used to help make the meaning of sentences clearer and to make them easier to read and understand. Punctuation marks can also be used to indicate pauses in speech, to create emphasis, and to indicate the speaker’s attitude. There are many different types of punctuation marks, each with its own purpose. The most commonly used punctuation marks are the period, comma, question mark, exclamation mark, quotation marks, and the apostrophe.
Quotation marks are used to enclose quoted material, while the apostrophe is used to indicate possession or to replace missing letters in a word or phrase. By using punctuation correctly, writers can ensure that their messages are correctly understood by their readers.
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Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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Tom’s yearly salary is $78000
Calculate Tom’s fortnightly income. (Use 26
fortnights in a year.)
Fortnightly income =
$
Tom's fortnightly income is $3000.
What is average?In mathematics, an average is a measure that represents the central or typical value of a set of numbers. There are several types of averages commonly used, including the mean, median, and mode.
To calculate Tom's fortnightly income, we need to divide his yearly salary by the number of fortnights in a year:
Fortnightly income = Yearly salary / Number of fortnights in a year
Fortnightly income = $78000 / 26 = $3000
Therefore, Tom's fortnightly income is $3000.
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question - Calculate the Tom's fortnightly income and yearly salary by the number of fortnights in a year .
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0°C and 1.08°C. Round your answer to 4 decimal places
Answer: We are given that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.
To find the probability of obtaining a reading between 0°C and 1.08°C, we need to calculate the z-scores for these values using the formula:
z = (x - mu) / sigma
where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.
For x = 0°C, we have:
z1 = (0 - 0) / 1.00 = 0
For x = 1.08°C, we have:
z2 = (1.08 - 0) / 1.00 = 1.08
Using a standard normal table or a calculator, we can find the probability of obtaining a z-score between 0 and 1.08.
Using a standard normal table or a calculator, we find that the probability of obtaining a z-score between 0 and 1.08 is 0.3583.
Therefore, the probability of obtaining a reading between 0°C and 1.08°C is 0.3583, rounded to 4 decimal places.
Step-by-step explanation:
se spherical coordinates to evaluate the triple integral where is the region bounded by the spheres and .
The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].
Given that the triple integral is-
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
E is the region bounded by the spheres which are,
[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]
In spherical coordinates we have,
x = r cosθ sin ∅
y = r sinθ sin∅
z = r cos∅
dV = r²sin∅ dr dθ d∅
E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,
1 ≤ r ≤ 3
0 ≤ θ ≤ 2π
0 ≤ ∅ ≤ π
Then
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]
The complete question is-
Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.
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Solve please geometry, solve for x
Answer: The answer is D
Step-by-step explanation:
Pythagorean theorem: a²+b²=c²
x²+x²=14²
2x²=196
Evaluate...
x=7√2
Find the standard normal area for each of the following Round your answers to the 4 decimal places
The standard normal areas are given as follows:
P(1.22 < Z < 2.15) = 0.0954. P(2 < Z < 3) = 0.0215.P(-2 < Z < 2) = 0.9544.P(Z > 0.5) = 0.3085.How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Considering the second bullet point, the areas are given as follows:
P(1.22 < Z < 2.15) = p-value of Z = 2.15 - p-value of Z = 1.22 = 0.9842 - 0.8888 = 0.0954.P(2 < Z < 3) = 0.0215 = p-value of Z = 3 - p-value of Z = 1 = 0.9987 - 0.9772 = 0.0215.P(-2 < Z < 2) = p-value of Z = 2 - p-value of Z = -2 = 0.9772 - 0.0228 = 0.9544P(Z > 0.5) = 1 - p-value of Z = 0.5 = 1 - 0.6915 = 0.3085.More can be learned about the normal distribution at https://brainly.com/question/25800303
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T/F. Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars.
The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.
The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.
On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.
Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.
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Mr. Nkalle invested an amount of N$20,900 divided in two different schemes A and B at the simple interest
rate of 9% p.a. and 8% p.a, respectively. If the total amount of simple interest earned in 2 years is N$3508,
what was the amount invested in Scheme B?
Answer:
Let's assume that Mr. Nkalle invested an amount of x in Scheme A and (20900 - x) in Scheme B.
The simple interest earned on Scheme A in 2 years would be:
SI(A) = (x * 9 * 2)/100 = 0.18x
The simple interest earned on Scheme B in 2 years would be:
SI(B) = [(20900 - x) * 8 * 2]/100 = (3344 - 0.16x)
The total simple interest earned in 2 years is given as N$3508:
SI(A) + SI(B) = 0.18x + (3344 - 0.16x) = 3508
0.02x = 164
x = 8200
Therefore, Mr. Nkalle invested N$8200 in Scheme A and N$12700 (20900 - 8200) in Scheme B. So the amount invested in Scheme B was N$12700.
are the ratios 2:1 and 20:10 equivalent
Yes, there is an analogous ratio between 2:1 and 20:10.
What ratio is similar to 2 to 1?We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.
By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.
As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.
The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:
20 ÷ 10 : 10 ÷ 10
= 2 : 1
As a result, both ratios have the same reduced form, 2:1, making them equal.
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Which expression represents the distance
between point G and point H?
|-12|16| |-12|+|-9|
1-9|-|-6|
|-12|+|6|
-15
H(-9,6)
G(-9,-12)
15+y
0
-15-
15
Answer:
Step-by-step explanation:
2
Will tracks the high and low tempters in his town for five days during a cold spell in January his results are shown in the table below
Days when change in temperature more than 10° F are Option B)Tuesday and E) Friday.
Define change in temperaturecalculating the difference by deducting the end temperature from the initial temperature. The temperature difference is therefore 75 degrees Celsius - 50 degrees Celsius = 25 if something begins at 50 degrees Celsius and ends at 75 degrees Celsius.
Change in temperature on Monday from High to low
=15-10=5°F
Change in temperature on Tuesday from High to low
=8-(-4)=12°F
Change in temperature on Wednesday from High to low
=-2-(-5)=3°F
Change in temperature on Thursday from High to low
=-3-(-7)=4°F
Change in temperature on Friday from High to low
=-1-(-12)=11° F
Days when change in temperature more than 10° F are Tuesday and Friday.
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The Complete question is attached below:
Find the generating functions and the associated sequences of: (x+4) ^ 4
Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
What is the generating functions and associated sequences of the functionTo find the generating function of (x+4)^4, we expand it using the binomial theorem:
[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
Therefore, the generating function of (x+4)^4 is:
[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.In this case, the sequence is given by the coefficients of G(x):a₀ = 256a₁ = 256a₂ = 96a₃ = 16a₄ = 1To find the generating function of (x+4)^4, we expand it using the binomial theorem:
(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)
where C(n,k) denotes the binomial coefficient "n choose k".
Simplifying the terms, we get:
(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256
Therefore, the generating function of (x+4)^4 is:
G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256
The associated sequence can be read off by finding the coefficients of each power of x:
The coefficient of x^k is the k-th term of the sequence.
In this case, the sequence is given by the coefficients of G(x):
a₀ = 256
a₁ = 256
a₂ = 96
a₃ = 16
a₄ = 1
Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.
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complete the table below.
4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569
Answer:
?
Step-by-step explanation:
A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
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For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answer:
Find f(g(x)) f(x)=7x-8 , g(x)=3x-2. f(x)=7x−8 f ( x ) = 7 x - 8 , g(x)=3x−2 g ( x ) = 3 x - 2. Step 1. Set up the composite result function. f(g(x)) f ( g ...
please mark me as a brainalist
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
pls help very soon
Answer:
We have two equations:
√x +2y^2 = 15 ----(1)
√4x - 4y^2=6 ----(2)
Let's solve for x:
From (1), we have:
√x = 15 - 2y^2
Squaring both sides, we get:
x = (15 - 2y^2)^2
Expanding, we get:
x = 225 - 60y^2 + 4y^4
From (2), we have:
√4x = 6 + 4y^2
Squaring both sides, we get:
4x = (6 + 4y^2)^2
Expanding, we get:
4x = 36 + 48y^2 + 16y^4
Substituting the expression for x from equation (1), we get:
4(225 - 60y^2 + 4y^4) = 36 + 48y^2 + 16y^4
Simplifying, we get:
900 - 240y^2 + 16y^4 = 9 + 12y^2 + 4y^4
Rearranging, we get:
12y^2 - 12y^4 = 891
Dividing both sides by 12y^2, we get:
1 - y^2 = 74.25/(y^2)
Multiplying both sides by y^2, we get:
y^2 - y^4 = 74.25
Let z = y^2. Substituting, we get:
z - z^2 = 74.25
Rearranging, we get:
z^2 - z + 74.25 = 0
Using the quadratic formula, we get:
z = (1 ± √(1 - 4(1)(74.25))) / 2
z = (1 ± √(-295)) / 2
Since the square root of a negative number is not real, there are no real solutions for z, which means there are no real solutions for y and x.
Therefore, the answer is "no solution".
Tell me which brand or which size is a better buy.
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
A type of wood has a density of 250 kg/m3. How many kilograms is 75,000 cm3 of the wood? Give your answer as a decimal.
Consider the function h(x) = a(−2x + 1)^5 − b, where a does not=0 and b does not=0 are constants.
A. Find h′(x) and h"(x).
B. Show that h is monotonic (that is, that either h always increases or remains constant or h always decreases or remains constant).
C. Show that the x-coordinate(s) of the location(s) of the critical points are independent of a and b.
Answer:
A. To find the derivative of h(x), we can use the chain rule:
h(x) = a(-2x + 1)^5 - b
h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4
To find the second derivative, we can again use the chain rule:
h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3
B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.
C. To find the critical points, we need to find where h'(x) = 0:
h'(x) = -10a(-2x + 1)^4 = 0
-2x + 1 = 0
x = 1/2
Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.
Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
What is function in mathematics?Function in mathematics is a relation between two sets, where one set is the input and the other set is the output. Functions are an important tool in mathematics and can be used to describe and model real-world phenomena. Functions take inputs, manipulate them and produce outputs. They can be used to represent relationships between two or more variables, or to represent a complex process. Functions allow us to break down complex problems into smaller, more manageable pieces and to study how changes in one variable affect other variables.
The function represented by the table is linear. It can be determined by the fact that the y-values change by the same amount every time the x-values increase by one unit. In this case, the y-values decrease by 2 each time the x-values increase by one unit. This is an example of a linear function.
Linear functions have the shape of a straight line and are characterized by having a constant rate of change. The constant rate of change is represented by the slope of the line, which in this case is -2. This means that for every one unit increase in the x-values, the y-values decrease by two.
A quadratic function is the opposite of a linear function, as it has a rate of change that is not constant. Quadratic functions are characterized by their parabolic shape and their rate of change increases as x-values increase. Exponential functions are characterized by their curved shape and increase exponentially as x-values increase.
In conclusion, the function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
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find the value of the derivative (if it exists) at
each indicated extremum
Answer:
The value of the derivative at (-2/3, 2√3/3) is zero.
Step-by-step explanation:
Given function:
[tex]f(x)=-3x\sqrt{x+1}[/tex]
To differentiate the given function, use the product rule and the chain rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Product Rule of Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{7 cm}\underline{Differentiating $[f(x)]^n$}\\\\If $y=[f(x)]^n$, then $\dfrac{\text{d}y}{\text{d}x}=n[f(x)]^{n-1} f'(x)$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Let}\;u &= -3x& \implies \dfrac{\text{d}u}{\text{d}{x}} &= -3\\\\\textsf{Let}\;v &= \sqrt{x+1}& \implies \dfrac{\text{d}v}{\text{d}{x}} &=\dfrac{1}{2} \cdot (x+1)^{-\frac{1}{2}}\cdot 1=\dfrac{1}{2\sqrt{x+1}}\end{aligned}[/tex]
Apply the product rule:
[tex]\implies f'(x) =u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}[/tex]
[tex]\implies f'(x)=-3x \cdot \dfrac{1}{2\sqrt{x+1}}+\sqrt{x+1}\cdot -3[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-3\sqrt{x+1}[/tex]
Simplify:
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{3\sqrt{x+1} \cdot 2\sqrt{x+1}}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x+6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{9x+6}{2\sqrt{x+1}}[/tex]
An extremum is a point where a function has a maximum or minimum value.
From inspection of the given graph, the maximum point of the function is (-2/3, 2√3/3).
To determine the value of the derivative at the maximum point, substitute x = -2/3 into the differentiated function.
[tex]\begin{aligned}\implies f'\left(-\dfrac{2}{3}\right)&=- \dfrac{9\left(-\dfrac{2}{3}\right)+6}{2\sqrt{\left(-\dfrac{2}{3}\right)+1}}\\\\&=-\dfrac{0}{2\sqrt{\dfrac{1}{3}}}\\\\&=0 \end{aligned}[/tex]
Therefore, the value of the derivative at (-2/3, 2√3/3) is zero.
Suppose the current cost of gasoline is $2.93 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
Answer:
Step-by-step explanation:
To find the current price index number using the 1975 price of 56.7 cents as the reference value, we can use the formula:
Price Index = (Current Price / Base Price) x 100
Where "Current Price" is the current cost of gasoline, and "Base Price" is the 1975 price of 56.7 cents.
Substituting the values given in the problem, we get:
Price Index = ($2.93 / $0.567) x 100
Price Index = 516.899
Therefore, the current price index number, using the 1975 price of 56.7 cents as the reference value, is 516.899.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than 0.35°C.
Round your answer to 4 decimal places
The probability of obtaining a reading less than 0.35° C is approximately 35%.
What exactly is probability, and what is its formula?Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.
The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.
To solve this problem, we must use the z-score formula to standardise the value:
[tex]$Z = \frac{x - \mu}{\sigma}[/tex]
Z = standard score
x = observed value
[tex]\mu[/tex] = mean of the sample
[tex]\sigma[/tex] = standard deviation of the sample
Here
x = 0.35° C
[tex]\mu[/tex] = 0° C
[tex]\sigma[/tex] = 1.00°C
Using the values on the formula:
[tex]$Z = \frac{0.35 - 0}{1}[/tex]
Z = 0.35
The probability of obtaining a reading less than 0.35° C is approximately 35%.
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If A = [ 1 2 4 0 5 6 ] and B= [ 7 3 2 5 1 9] find C= A+B and D=A-B
Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]
Step 2: To find C = A+B, add each element of A and B together.
C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]
C = [8, 5, 6, 5, 6, 15]
Step 3: To find D = A-B, subtract each element of B from A.
D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]
D = [-6, -1, 2, -5, 4, -3]
What was your recommended intake of carbohydrates (grams), and how far were you from it? Show the mathActual Intake Recommended Intake Percentage159.00 115-166 100%
The actual intake of carbohydrates is 138% as compare to recommended intake.
Recommended intake of carbohydrates or any other nutrient are,
Based on the information provided,
Consumed 159 grams of carbohydrates,
Recommended intake is between 115 and 166 grams.
Calculate the percentage of actual intake compared to the recommended intake, use the following formula,
Percentage = (Actual Intake / Recommended Intake) x 100%
Substituting the values in the formula we have,
⇒Percentage = (159 / 115) x 100%
⇒Percentage ≈ 138.3%
Therefore, the actual intake of carbohydrates is about 138% of the recommended intake, indicating that consumption of more carbohydrates than recommended.
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
