Answer:
1025
Step-by-step explanation:
y=5x
y=5(205)
y=1025
The 205th term in the arithmetic sequence is 1025.
We have,
To find the 205th term in the sequence 5, 10, 15, 20, 25 ..., we can use the formula for an arithmetic sequence:
The nth term of an arithmetic sequence can be represented as:
[tex]a_n = a_1 + (n - 1) ~d[/tex]
Where:
[tex]a_n[/tex] is the nth term,
[tex]a_1[/tex] is the first term,
n is the position of the term we want to find, and
d is the common difference between consecutive terms.
In this sequence, the first term [tex]a_1[/tex] is 5, and the common difference (d) is 10 - 5 = 5.
Now, let's find the 205th term ([tex]a_{205}[/tex]):
= 5 + (205 - 1) * 5
= 5 + 204 * 5
= 5 + 1020
= 1025
Thus,
The 205th term in the arithmetic sequence is 1025.
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Factor the GCF:-12x4y - 9x³y² + 3x²y³ (5 points)
O-3x²y(4x2 + 3xy - y²)
O 3x²y(-4x² + 3xy - y²)
O-3(4x²y + 3x³y² - x²y³)
O-3x²y(-4x2-3xy + y²)
Answer:
A. 3x^2y(4x2 + 3xy - y^2)
Step-by-step explanation:
-12(x^4)y - 9x³y² + 3x²y³
-3x²y(4x² + 3xy - y²)
A company currently pays a dividend of $2.6 per share (d0 = $2.6). it is estimated that the company's dividend will grow at a rate of 24% per year for the next 2 years, and then at a constant rate of 8% thereafter. the company's stock has a beta of 1.8, the risk-free rate is 7.5%, and the market risk premium is 4.5%. what is your estimate of the stock's current price?
The current value of the stock is $53.413455.
What is the CAMP model?The CAMP model describes the relationship between systemic risk, or the general dangers of investing, and projected return on assets, specifically stocks.To find the current price of stock:
Stock’s current price: 53.41 dollars
First, we determine the stock's value using the CAPM model.
Ke = rf + (rm - rf)risk free, rf = 0.085.premium market = (rm - rf) = 0.045(nondiversifiable risk) = 1.3Then, Ke = 0.085 + 1.3(0.045).
Ke = 0.14350The current value of the future dividends must now be known:
D0 = 2.8D1 = D0 x (1 + g) = 2.8 * 1.23 = 3.444D2 = 3.444 x 1.23 = 4.2361200The next dividends, which are at perpetuity will be solved using the dividend growth model:
dividends/return-growth = Intrinsic valueIn this case, dividends will be:
4.23612 x 1.07 = 4.5326484Return will be calculated using the CAPM and g = 7%.
plug this into the Dividend grow model,
4.53264840.1435-0.07 = Intrinsic ValueValue of the dividends at perpetuity: 61.6686857Finally, it's crucial to remember that these statistics were calculated for the present year.
We must bring them to the present day using the present value of a lump sum:
principal/(1 + rate)time = PV3.444/(1 + 0.1435)1 = PV3.011805859 = PV4.23612/(1 + 0.1435)2 = PV3.239633762 = PV61.6686857/(1 + 0.1435)2 = PV47.16201531 = PVWe add them and get the value of the stock, 53.413455
Therefore, the current value of the stock is $53.413455.
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5. If a, s are the zeroes of 2 -8x +λ ,such that a – s = 2, then λ=
The value of λ = 8s + 6
What are the zeroes of a function?The zeroes of a function f(x) are the values of x at which f(x) = 0.
How to find λ?Given that a, s are the zeroes of 2 - 8x + λ ,such that a - s = 2.
Since we require λ,
So, let f(x) = 2 - 8x + λ.
At x = a, f(x) = 0.
So, substituting the value of x = a into f(x), we have
f(a) = 2 - 8a + λ
Since f(a) = 0, we have
2 - 8a + λ = 0
2 + λ = 8a (1)
Also, x = s, f(x) = 0.
So, substituting the value of x = s into f(x), we have
f(s) = 2 - 8s + λ
Since f(s) = 0,we have
2 - 8s + λ = 0
2 + λ = 8s (2)
Since a - s = 2
Making a subject of the formula, we have
⇒ a = s + 2
So, substituting the value of a into equation (1), we have
2 + λ = 8a (1)
2 + λ = 8(s + 2) (1)
2 + λ = 8s + 16
- 14 + λ = 8s (3)
Adding equation (2) and (3), we have
-14 + λ = 8s (3)
+
2 + λ = 8s (2)
-12 + 2λ = 16s
2λ = 16s + 12
Dividing through by 2, we have
2λ/2 = (16s + 12)/2
λ = 4(4s + 3)/2
λ = 2(4s + 3)
λ = 8s + 6
So, the value of λ = 8s + 6
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Which equation represents y = −x2 + 4x − 1 in vertex form?
The vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
How to determine the vertex form of the quadratic equation?The quadratic equation is given as:
y = -x^2 + 4x - 1
Differentiate the above quadratic equation.
This is done with respect to x by first derivative
So, we have:
y' = -2x + 4
Set the derivative to 0
-2x + 4 = 0
Subtract 4 from both sides of the equation
-2x + 4 - 4 = 0 - 4
Evaluate the difference in the above equation
-2x = -4
Divide both sides of the above equation by -2
x = 2
Rewrite as
h = 2
Substitute 2 for x in the equation y = -x^2 + 4x - 1
y = -2^2 + 4 *2 - 1
Evaluate the equation
y = 3
Rewrite as:
k = 3
A quadratic equation in vertex form is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x - 2)^2 + 3
In the equation y = -x^2 + 4x - 1, a = -1
So, we have:
y = -(x - 2)^2 + 3
Hence, the vertex form of the equation y = -x^2 + 4x - 1 is y = -(x - 2)^2 + 3
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30 POINTS HELP PLS!!!!!!!
i really hate how we actually have to type something.
Boyle's law states that if the temperature of a gas remains constant, then PV=c, where P=pressure,V=volume , and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 10in^3/sec, at what rate is P increasing when P =60lb/in^2 and V=20in^3 in? (do not round your answer.)
a. 30 lb/in^2 per sec
b. 120lb/in^2 per sec
c. 9 lb/in^2 per sec
d. 10/3 lb/in^2 per sec
The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B
Boyle's lawPV = c
where,
P=pressure,V=volume , and c is a constantwhen P =60lb/in^2 and V=20in^3
PV = c
60 × 20 = 1200 in
Find P if V is decreasing at a rate of 10in^3/sec
PV = c
P × 10 = 1200
10P = 1200
P = 1200 / 10
P = 120lb/in^2 per sec
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Find the area in square units of ABC△ plotted below.
Answer:
71
Step-by-step explanation:
A mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row. How many distinct arrangements are possible
This relates to combination and permutations and the number of distinct arrangements that are possible will be 6.
How to illustrate the information?From the information, a mathematical prodigy wishes to put 2 of his indistinguishable IMO gold medals and 2 of his indistinguishable IPhO gold medals in one row.
Let 1 = IMO
Let 0 = IPho.
Therefore, the number of arrangement will be:
0011
0110
1100
1010
0101
1001
Therefore, the number of arrangement will be 6.
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I need help with trigonometry
Again..
Answer: C. - √2
Step-by-step explanation:
Given requirements from the question
Find the exact value of sec 135°
Convert into common trigonometric expression
sec = secant
secx = 1 / cosx
Therefore, sec 135° = 1 / (cos 135°)
Find the reference angle
135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.
Since 135° is in the second quadrant, its reference angle will be
180° - 135° = 45°
However, we need to consider the positive and negative.
In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.
Therefore, when the value of cosine is in QII, it is negative.
The reference angle = - (1 / cos 45°)
Determine the final value
Given that the reference angle = - (1 / cos 45°)
cos 45° = 1 / √2
Therefore:
sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
which number set(s) does -10 belong to
irrational numbers
whole numbers
rational numbers
integers
real numbers
counting or natural numbers
No number set describes this number.
The number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E
Number sets of negative numbersA rational number can be defined as a number expressed as the ratio of two integers, where the denominator is not be equal to zer0
- 10 can be written as = 1/ 10
Integers are whole number that could be positive, negative and even zero
- 10 is a negative whole number
Real numbers are numbers with continuous quantity that can represent distance along a number line
-10 can represent distance along a number line.
Thus, the number set(s) that - 10 belong to are rational numbers, integers and real numbers. Option C, D and E
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On a rectangular soccer field, Sang is standing on the goal line 20 yards from the corner post. Jazmin is standing 99 yards from the same corner post on the nearest adjacent side of the field. What is the distance from Sang to Jazmin?
A. 119
B. 101
C. 10,201
D. 1,980
The distance from Sang to Jazmin is 101 yards.
What is the distance from Sang to Jazmin?
From the discussion in the question, we can see that the positions of Sang and Jazmin can be construed to give a rectangle. We know that the rectangle is a four sided figure.
The diagonal is a line that is drawn from one side of the four sided figure to another. Hence we can be able to apply the Pythagoras theorem to obtain the distance from Sang to Jazmin.
From;
c^2 = a^2 + b^2
c = √a^2 + b^2
c = √(20)^2 + (99)^2
c = 101 yards.
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Choose the numbers that are terminating decimals. Select all that apply.
A. 0.032
B. 0.999...
C. 0.525
D. 0.75
Answer: A, C, and D
Step-by-step explanation:
A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.
✓ A. 0.032
✗ B. 0.999...
✓ C. 0.525
✓ D. 0.75
25 Points please help me
ASAP and I will mark brainlyist
Answer:
(a)
1. 4.6... sample mean2. 4.6.. sample mean3. 4.8... sample mean4. 5.2... sample mean(b) range of sample means =0.6
(c)
FalseFalseFalseFalseThe table below shows the birth rate (per 1000) per year in the United States according to data from the National Center for Health Statistics. Let x represent the number of years since 2000 with x = 0 representing the year 2000. Let y represent the birth rate per 1000 population. Write the slope-intercept form of the equation for the line of fit using the points representing 2001 and 2010. Round to the nearest hundredth.
The regression linear function, in slope-intercept form, is given by:
y = -0.07x + 14.5
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points are given as follows:
(0, 14.7), (1, 14.5), (2, 14.4), (3, 14.1), (4, 14), (5, 14.1), (6, 14.1), (7, 14.2), (8, 14), (9, 13.8), (10, 14).
Inserting these points into a calculator, the regression linear function, in slope-intercept form, is given by:
y = -0.07x + 14.5
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Answer:
y = -0.07x + 14.5
Step-by-step explanation:
How should I solve this?
The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;
[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]
Which method can be used to prove the given relation?From the given information, we have;
∆ABD ~ ∆PQD∆CDB ~ ∆PQBAccording to the ratio of corresponding sides of similar triangles, we have;
[tex] \frac{x}{z} = \mathbf{\frac{BD}{QD} }[/tex]
[tex] \frac{y}{z} = \frac{BD}{ BQ} [/tex]
Which gives;
[tex] \mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D} [/tex]
[tex] \frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}[/tex]
QD × x = BD × z
BD × z = (1 - QD/BD) × y = y - (QD × y/BD)
Therefore;
BD × z = y - (QD × y/BD)
BQ × y = y - (QD × y/BD)
BQ × y = y - (z × y/x) = y × (1 - z/x)
(1 - z/x) = BQ
BD × z = y × (1 - z/x)
BD = (y × (1 - z/x))/z
Therefore;
QD × x = y × (1 - z/x)
(BD-BQ) × x = y × (1 - z/x)
(BD-(1 - z/x)) × x = y × (1 - z/x)
BD = (y × (1 - z/x))/x + (1 - z/x)
BQ + QD = (1 - z/x) + (y × (1 - z/x))/x
BD = BQ + QD
(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z
(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z
Dividing both sides by (1 - z/x) gives;
y/x + 1 = y/z
Dividing all through by y gives;
(y/x + 1)/y = (y/z)/y
1/x + 1/y = 1/zTherefore;
[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]
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Show how 60/90 becomes 2/3
60 ÷ 30 = 2
and
90 ÷ 30 = 3
---> 60/90 = 2/3
❄ Hi there,
the way 60/90 becomes 2/3 is this:
The fraction's numerator & denominator are both divided by 30:[tex]\sf{\dfrac{60\div30}{90\div30}=\dfrac{2}{3}}[/tex]
That's it!
❄
The image of the point P(-3, 2) under the translation (2/1) is
The image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)
How to determine the image of the translation?The coordinate point is given as:
P = (-3, 2)
The translation is given as
T<2,1>
The translation can be represented as:
(x, y) = (x + 2, y + 1)
So, we have the following equation
P' = (-3 + 2, 2 + 1)
Evaluate the sum
P' = (-1, 3)
Hence, the image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)
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in april 2005, roland mailed a package from his local post office in Albermarle, NC ro a friend in fishers, Indiana for $2.76 per ounce. The first class domestic rate at the time was $.23 per ounce. Write and solve an equation to determine the weight of the package
The weight of the package is 12 ounces
How to solve an equation to determine the weight of the package?The given parameters are
Total amount = $2.76
Domestic rate = $.23 per ounce
The equation to determine the weight of the package is represented as:
Weight = Total amount/Domestic rate
Substitute the known values in the above equation
Weight = 2.76/.23
Evaluate the quotient
Weight = 12
Hence, the weight of the package is 12 ounces
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magan wants to ride his bicycle 30.4 miles this week. he has already ridden 4 miles if he rides for 4 more days what is the average number of miles he would have to ride each day to meet his goal?
The average number of miles he will ride each day to meet his goal is 6.6 miles
How to find the average number of miles she will ride?He wants to ride his bicycle 30.4 miles this week.
He has already ridden 4 miles.
He rides 4 more days.
Therefore, the average number of miles he would have to ride each day to meet his goal can be calculated as follows:
let
x = number of miles driven
Hence, the equation can be represented as follows;
4x + 4 = 30.4
Therefore,
4x + 4 = 30.4
4x + 4 - 4 = 30.4 - 4
4x = 26.4
x = 26.4 / 4
x = 6.6
Therefore, the average number of miles he will ride each day to meet his goal is 6.6 miles
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Which of the following is a solution to the equation
3/4
x-12 = -18?
1) 4.5
2) -8
3) -22.5
4) -40
Answer: B) -8
Step-by-step explanation:
We add 12 both sides
3/4 x = -18 + 12Add −18 and 12 to get −6.
3/4 x = -6Multiply both sides by 3/4 by the reciprocal of 3/4.
x = -6 × (3/4)Express a -6 x (3/4) as a single fraction.
x = -6 × 4 / 3Multiply −6 and 4 to get −24.
x = -24 / 3Divide −24 by 3 to get −8.
x = -8Answer: Option "2" is correct. ✅
Find the Z-scores that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution.
The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.
Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.
In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:
Z=(X-μ)/σ
It is used to measure how many standard deviations the measure is from the mean.
After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.
The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.
Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.
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Show the following linear expression. Show all of your work and identify any properities used.
7-6x-9-x+3
Answer:
-7x + 1
Associative Property can be used.
Step-by-step explanation:
Hello!
We can simply the expression by combining like terms.
Like terms are terms with the same variable and degree. They may have different coefficients.
Simplify7 - 6x - 9 - x + 37 - 9 + 3 - 6x - x1 - 7xThe simplified form is 1 - 7x, or -7x + 1.
We can also represent this using the Associative property, by grouping like terms:
7 - 6x - 9 - x + 3(7 - 9 + 3) + (-6 - x)1 + (-7x)-7x + 1The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?
Answer: 180 meters
Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.
2
5. One flight took a total of 4.6 hours. Write this number as a mixed number
and as an improper fraction. Show your work in the space below. Remember
to check your solution.
Step-by-step explanation:
4.6 hrs is 46over 10 which is
13 over 5 or 2 and 3over 5
How many ways are ther eto line up the 12 people if the bride must be next to the maid of honor?
the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.
How to determine the permutationThe formula for finding the number of arrangement is given as;
Permutation = [tex]\frac{n!}{n - r!}[/tex]
Where;
n is the total number of objectr is the number of selected objectsFrom the question given, we can deduce that
n = 12 people
r = 2, because they must come next to each other and is taken as 2
We then have,
Permutation = [tex]\frac{12!}{12 - 2!}[/tex]
Permutation = [tex]\frac{12!}{10!}[/tex]
Permutation = 132 ways
This is to tell us that the number of ways to arrange the people is 132 ways
Thus, the number of ways to line up the 12 people if the bride must be next to the maid of honor is 132 ways.
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I NEED HELP WITH MY MATH PLEASE
A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500?
The balance after 8 years is $22,942.67
What is the balance after 8 years?
We know that the savings account earns 15% annually, and the initial deposit is $7500, then the balance as a function of time in years is:
B = $7500*(1 + 15%/100%)^t
B = $7500*(1.15)^t
The balance after 8 years is what we get when we evaluate the above function in t = 8, so we get:
B = $7500*(1.15)^8 = $22,942.67
So the correct option is the last one.
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(MID SCHOOL ALGEBRA)
can somebody explain to me from this image, why the -13x and +6 becomes +13x and -6?
Answer:
- (2x^2 - 13x + 6)
The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.
what is 4.22 x 10^17 seconds
We can rewrite the given time as:
7.03x10^15 mins 1.17x10^14 hours.4.88x10^12 days.What is 4.22x10^17 seconds in minutes and hours?First, remember that:
60s = 1 min
Then to write that amount in minutes, we just need to divide by 60, so we get:
(4.22x10^17)/60 mins= 7.03x10^15 mins
Now, remember that:
1 hour = 3600s
Then to get the time in hours, we need to divide by 3600:
(4.22x10^17)/3600 h = 1.17x10^14 hours.
Similarly, you can change to any time unit that you want, for example:
1 day = 24*3600 s
Then the time in days is:
(4.22x10^17)/(24*3600) days = 4.88x10^12 days.
And so on.
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The diameter of a circle graphed in the xy-plane has endpoints at (-2, -1) and (4,7). Which of the following is an equation of the circle?
A (x + 1)² + (y + 1)² = 25
B (x + 1)² + (y + 1)² = 100
C (x - 1)² + (y - 3)² = 100
D (x - 1)² + (y - 3)² = 25
The required equation of the circle whose endpoint of the diameter (-2, -1) and (4,7) is (x - 1)² + (y - 3)² = 25 . Option D is correct.
Given that,
The endpoints of the circle's diameter (-2, -1) and (4,7).
The equation of the circle is to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r².
where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.
Center of the circle(h, k) = (-2 + 4)/2 ,(-1+7)/2
= 1 , 3
Radius of the circle,
[tex]r^2 =\sqrt{(1+2)^2+(3+1)^2}\\r^2 =\sqrt{9+16} \\r^2 = 25[/tex]
Equation of the circle with center (1, 3)
[tex]r^2 = (x - 1)^2 + (y-3)^2[/tex]
[tex]25 = (x - 1)^2 + (y-3)^2[/tex]
Thus, the required equation of the circle whose endpoint of the diameter (-2, -1) and (4,7) is (x - 1)² + (y - 3)² = 25 . Option D is correct.
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