Answer:
A. -2.7, -9, -30, -100, ...
B. -1, 2.5, -6.25, 15.625, ...
C. 9.1, 9.2, 9.3, 9.4, ...✔️
D. 8, 0.8, 0.08, 0.008, ...✔️
E. 4, -4, -12, -20, ... ✔️
Hope you understand
Let me know if you need further explaination
A certain sum of money at simple interest amount to $1300 in 4 years and to $1525 in 7 years. Find the sum and the rate percent
Answer:
P((1 + r)^4) = 1,300
P((1 + r)^7) = 1,525
-----------------------
(1 + r)^3 = 61/52, so r = .0547 = 5.47%
P(1.0547^4) = 1,300, so P = $1,050.78
Find the final amount in the following retirement account in which the rate of return on the account and regular contribution change over time.
$213 per month invested at 4% compounded monthly, for 4 years; then $348 per month invested at 7% compounded monthly for 4 years
The final amount in the retirement account in which the rate or return and the regular contributions change over time is $33,844.51.
How the final amount is determined:To determine the final amount in the retirement account, we first compute the future value of the periodic deposits of $213 for 4 years, using an online finance calculator.
The future value of $213 deposited for 48 months is used as the present value of the investment for the next 4 years or 48 months.
Then, with the present value and the periodic deposits, the final amount (future value) of the retirement account is determined as follows:
Future Value of $213:N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
PMT (Periodic Payment) = $213
Results:
FV = $11,067.40
Sum of all periodic payments = $10,224.00
Total Interest $843.40
Final Value:N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 7%
PV (Present Value) = $11,067.40
PMT (Periodic Payment) = $348
Results:
Final Value (FV) = $33,844.51
Sum of all periodic payments = $16,704.00
Total Interest = $6,073.11
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6. find the open intervals where the function is concave up and concave down.
Show steps
Answer:
Concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).
Step-by-step explanation:
To find the intervals where the function y = -cot(x) is concave up and concave down, we need to find the second derivative of the function and then determine its sign for different intervals.
First, we find the first derivative of y = -cot(x):
dy/dx = csc^2(x)
Then, we find the second derivative by differentiating the first derivative:
d^2y/dx^2 = -2csc^2(x) * cot(x)
We know that the function is concave up when the second derivative is positive, and concave down when the second derivative is negative.
Now, we need to determine the intervals where the second derivative is positive and negative.
d^2y/dx^2 > 0 when:
-2csc^2(x) * cot(x) > 0
csc^2(x) < 0 and cot(x) < 0 or csc^2(x) > 0 and cot(x) > 0
Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is positive when cot(x) > 0.
d^2y/dx^2 < 0 when:
-2csc^2(x) * cot(x) < 0
csc^2(x) > 0 and cot(x) < 0 or csc^2(x) < 0 and cot(x) > 0
Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is negative when cot(x) < 0.
Recall that cot(x) = cos(x)/sin(x), which changes signs at x = kπ, where k is an integer.
So, we can now use this information to determine the intervals of concavity:
For x in (-π/2,0) and (0,π/2), cot(x) is positive and therefore, the function is concave up.
For x in (-π,-π/2) and (π/2,π), cot(x) is negative and therefore, the function is concave down.
Therefore, the function y = -cot(x) is concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).
Solve the two simultaneous equations.
You must show all your working.
3t+2p=15.5
5t+4p=28.5
Answer:
Given equations are,
5x+2y=−2 (1)
3x−5y=17.4 (2)
Multiply equation (1) by 5 and equation (2) by 2, we get,
5(5x+2y)=5×−2
∴25x+10y=−10 (3)
2(3x−5y)=2×17.4
∴6x−10y=34.8 (4)
Adding equations (3) and (4), we get,
31x=24.8
∴x=
31
24.8
Put this value in equation (1), we get,
5(
31
24.8
)+2y=−2
∴
31
124
+2y=−2
∴2y=−2−
31
124
∴2y=
31
−186
∴y=
31
−93
Step-by-step explanation:
What percent of the months of the year begin with the letter J
Answer:
25%
Step-by-step explanation:
What percent of the months of the year begin with the letter J?
January, June, and July
are 3 months out of 12, which equals 1/4 (12 : 3 = 4),
1/4 equals 25% (100 : 4 = 25%)
17. Rob purchased a boat three years ago. The boat decreased by 7% each year. Three years
later, the value of the boat was $32,174.28. Which equation initially models the value of Rob's
boat?
A. y = 40,000(0.93)*
B. y = 40,000(1.07)*
C. y = 32,174.28 (0.93)*
D. y = 32,174.28 (1.07)*
Answer:
The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.
Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:
y = 40,000(0.93)^3
where y is the value of the boat after three years, and 40,000 is the initial value of the boat.
Simplifying this equation, we get:
y = 40,000(0.7951)
y = 31,804
However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.
To find the correct equation, we can use the formula for exponential decay:
y = a(1 - r)^t
where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.
In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.
So we can set up an equation:
32,174.28 = 40,000(0.93)^3
Simplifying this equation, we get:
32,174.28 = 31,804.00
This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:
y = 40,000(0.93)^t
where t is the time in years.
Kim had 2 1/3 pounds of candy. Eric eats 2/5 of Kims candy. How much candy did Eric eat?
The quantity of candy that Eric ate would be = 14/15
How to calculate the quantity of candy eaten by Eric?The quantity of Candy Kim had = 2⅓ pounds.
The quantity of Kims candy that Eric ate = 2/5
That is 2/5 of 2⅓.
The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15
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cises
1. Yesterday the Rockville Corporation instituted a 2-for-1 stock split. Before the split, the market
share price was $63.44 per share and the corporation had 2.3 billion shares outstanding.
a. What was the pre-split market cap for Rockville?
b. What was the post-split number of shares outstanding for Rockville?
c. What was the post-split market price per share for Rockville?
a: $145,912,000,000
b: 4.6 bn shares
c: $31.72/per share (divide in half)
Helpppppppppppp meeeeeeeeeeeee
Answer:
2.25 units³
Hope this helps!
Step-by-step explanation:
The formula, base, and height are already given so all you have to do is multiply 2 with [tex]3\frac{3}{8}[/tex].
2 × [tex]\frac{9}{8}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25 units³
Which system of equations has a solution of (1, 2, 3)?
A. -2 - 2z = -8
Y+3z = 7
x + y m - -3x= -3
B. x + y + 2z = 9
2x + 2y + 3z = 15
x - z = -2
C. -3x + 2y + z = 4
X + y + 2z
X - y - z = -2
D. X + Y = 3
Y - z = 1
X + y - z = 0
Please I really need this class to graduate and I have no idea how to do this
Find the value of X
The value of x in the intersecting secant and tangent lines is 40 degrees
Finding the value of xFrom the question, we have the following parameters that can be used in our computation:
Intersecting secant and tangent lines
Using the theorem of intersecting secant and tangent lines, we have
x = 1/2 * difference of the arcs
Substitute the known values in the above equation, so, we have the following representation
x = 1/2 * (170 - 90)
Evaluate
x = 40 degrees
Hence, the value of x is 40
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Simplify sqrt(27) \cdot sqrt(12) \cdot sqrt(147)
Answer:
Step-by-step explanation:
what is the probability that a random point on AK will be on BE? pls help me
The probability that a random point on the AK line will be on the BE line is 0.5 or 50%, since the length of the BE line is 10 units and the length of the AK line is 20 units.
To find the probability that a random point on the AK line will be on the BE line, we need to determine the length of the BE line and the length of the AK line.
The BE line extends from point -5 to point 5, a distance of 5 - (-5) = 10 units.
The AK line extends from point -10 to point 10, a distance of 10 - (-10) = 20 units.
Therefore, the probability that a random point on the AK line will be on the BE line is
Length of BE line / Length of AK line = 10 / 20 = 0.5
So, the probability that a random point on the AK line will be on the BE line is 0.5 or 50%.
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Find x and y in terms of a and b.
Sax + by = 0
x + y = 2
(x, y) =
(a + b)
Convert the given Cartesian equation into a polar equation.
x2+y2=2y
Answer: r=2sinθ.
Step-by-step explanation:To convert to polar coordinates, we use the relationships
xy=rcosθ=rsinθ.
Substituting these into the given equation, we find
x2+y2(rcosθ)2+(rsinθ)2r2cos2θ+r2sin2θ=2y=2(rsinθ)=2rsinθ
Factoring and applying the Pythagorean identity, we obtain
r2(cos2θ+sin2θ)r2(1)r2=2rsinθ=2rsinθ=2rsinθ
Dividing both sides by r yields
r2rr=2rsinθr=2sinθ
Thus, a polar equation representing the given function is r=2sinθ.
For questions 3-4, use the graph of the polynomial function to find the factorization of the polynomial. Assume there is no constant term. 3
3. The factored polynomial is p(x) = (x - 1)(x - 5)
4. The factored polynomial is p(x) = (x + 3)²
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.
This implies that its factors are (x - 1) and (x - 5)
So, the factored polynomial is p(x) = (x - 1)(x - 5)
4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots
This implies that its factors are (x - (-3)) = (x + 3) twice
So, the factored polynomial is p(x) = (x + 3)²
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I don't know how to do.
John is taking a true/false quiz. There are 4 questions. How many outcomes?
Answer:
16
Step-by-step explanation:
2×2×2×2=16
So, the answer is 16.
Justin makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The product of two negative integers is a negative integer.
Answer:
False. The product of two negative integers is a positive integer.
The diameter of a circle is 9cm. Find its area to the nearest whole number
Lydia has half of her investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If her total annual interest is $420 , how much does she have invested?
The total investment done by Lydia when her total annual interest is $420 at 11% dividend and 14% interest is equal to $3360.
Total annual interest = $420
Half of the investment in stock paying = 11% dividend
Half of the investment in stock paying = 14% interest
Let x be the amount Lydia has invested in each stock.
Since she has half of her investments in each stock,
The following system of equations to represent the situation,
Total annual interest is $420.
This implies ,
0.11x + 0.14x = 420
And total investment is,
x + x = 2x
Simplifying the first equation, we get,
⇒ 0.25x = 420
Dividing both sides by 0.25, we get,
⇒ x = 1680
So, Lydia has invested $1680 in each stock, for a total investment of,
⇒ 2x = 2(1680)
= 3360
Therefore, Lydia has a total investment of $3360.
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A new drug claims to reduce the number of epileptic seizures an individual with epilepsy diagnosed before the age of 4 years
old. In a study on the effectiveness of the new drug, 300 subjects were given the new drug and another 300 subjects were
given a placebo.
At the end of the 1-year study, the group given the new drug reported an average of 1.3 epileptic in the year. The group given the
placebo reported an average of 3.1 epileptic seizures in the year.
The data from the study are rerandomized 10 times. The difference of the means from rerandomization are
1.2, 2.4, 1.8, 1.3, 2.1, 0.9, 1.5, 0.7, 2.1, and 2.3.
What is the most appropriate conclusion about the new drug to draw from this information?
The new drug appears to reduce epileptic seizures since the rerandomized mean differences are considerably less
than the mean difference found between the two groups studied.
The new drug does not appear to reduce epileptic seizures since the rerandomized mean differences are close to
the mean difference found between the two groups studied.
The new drug does not appear to reduce epileptic seizures since the rerandomized mean differences are
considerably less than the mean difference found between the two groups studied.
The new drug appears to reduce epileptic seizures since the rerandomized mean differences are close to the mean
difference found between the two groups studied.
The new drug appears to reduce epileptic seizures since the rerandomized mean differences are close to the mean difference found between the two groups studied.
How to find the oprionThe rerandomized mean differences are:
1.2, 2.4, 1.8, 1.3, 2.1, 0.9, 1.5, 0.7, 2.1, and 2.3.
Several of these values are close to the observed mean difference of 1.8, which suggests that the observed difference could be due to chance alone.
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In the picture below, find the length of JK
The length of the secant line JK is 32.
What is the length of JK?The secant-tangent power theorem states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the diagram:
Tangent line JI = 24
External part of the secant segment LJ = 18
Secant segment JK = x + 18
Plug these values into the above formula and solve for b.
( tangent segment )² = External part of the secant segment × Secant segment.
24² = 18 × ( x + 18 )
576 = 18x + 324
18x = 576 - 324
18x = 252
x = 252/18
x = 14
Hence, secant line JK will be:
x + 18 = 14 + 18 = 32
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What is 1 1/4miles+1 3/8 miles = how far does Fred run in total?
Answer:
Fred doesn't run
Step-by-step explanation:
Fred doesn't run, Fred likes to walk, you obviously don't know Fred enough to answer this question, so tell your teacher how you can get in touch with Fred for a better relationship
let's firstly convert the mixed fractions to improper fractions, then sum them up.
[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{3}{8}} \implies \cfrac{1\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{11}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}+\cfrac{11}{8}\implies \cfrac{(2)5~~ + ~~(1)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{10+11}{8}\implies \cfrac{21}{8}\implies 2\frac{5}{8}~miles[/tex]
Tom took a trip of 1,300 miles. He traveled by train at 50 miles an hour and the same number of hours by plane at 275 mph. How many hours did the trip take?
3 hours
8 hours
4 hours
Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.
We have,
Let's call the number of hours Tom traveled by train t.
Since he traveled the same number of hours by plane, he also traveled for t hours at 275 mph.
The total distance he traveled is given by the sum of the distances traveled by train and by plane:
Distance by train = 50t
Distance by plane = 275t
Total distance = 1300
So we can set up the equation:
50t + 275t = 1300
Simplifying and solving for t, we get:
325t = 1300
t = 4
Therefore,
Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.
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Please help I keep getting 3.14
(Photo below)
Answer: 3.1
Step-by-step explanation: they are giving you the diameter so you halve it then you multiply it my 3.14 (pi) then you round it to the nearest tenth which is the 1 so you look to the left and it's not bigger than 5 so you round down so it stays as a 1
Help me pleaseeeeee
Question:
1. Describe a situation or a case btw 2 people then rephrase it to show empathy
According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.
What is the situation?The situation is: two friends are having an argument because one of them forgot to invite the other to a party.
Situation with empathyI can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.
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please answer soon I really need it.
consider this right triangle and find the exact length of the missing side
Answer:
6.324555320336759
Step-by-step explanation:
To find a missing leg in a right triangle use Pythagorean Theorem.
a^2 + b^2 = c^2 Substitution
6^2 + 2^2 = c^2 Simplify
36 + 4 = c^2 Simplify
40 = c^2 Simplify
6.324555320336759 = c
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
m²
14 m
2 m
The lateral surface area of the cylinder is approximately 175.84 square meters.
We have,
The lateral surface area of a cylinder.
= 2πrh
where r is the radius of the base, h is the height of the cylinder, and π is approximately 3.14.
Now,
r = 2 m, h = 14 m
Substituting these values in the formula, we get:
Lateral surface area = 2πrh
= 2 x 3.14 x 2 x 14
= 175.84 m² (rounded to the nearest tenth)
Therefore,
The lateral surface area of the cylinder is approximately 175.84 square meters.
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