The required rate of simple interest is 1.75%.
Here, we have,
(Principal + Interest) is a straightforward interest equation.
A = P(1 + rt)
Where: A is the sum of the accrued principal and interest.
Principal Amount is P.
I is the interest rate.
r is the annual percentage rate of interest, or R/100.
R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.
Since I = Prt,
the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,
which may be represented as A = P(1 + rt).
Given: Principal is $1,300
Rate is 7% and the amount earned that is A-P is $159.25.
A = P(1 + rt)
Therefore substituting the values in the above mentioned equation, we get:
159.25= 1300(1+r×7)
On solving we get,
r= 1.75%
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complete question:
At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.
What rate of simple interest is offered at the
Blue Bank?
A car and a plane are racing each other. Both start at the same position, with the plane being 500m above the car. The car has a maximum speed of 200km/h and the plane has a maximum speed of 300km/h. What is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?
-63.63 m/s is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?
Let's use the Pythagorean theorem to relate the distance between the car and the plane to their individual distances traveled. Let d be the distance traveled by the car, then the distance traveled by the plane is d + 70 (since the plane is ahead by 70m). Then, the distance between them is given by:
distance = [tex]\sqrt{d^{2}+500^{2} }[/tex] (using Pythagorean theorem)
Now, let's differentiate both sides with respect to time (t) to find the rate of change of the distance between the car and the plane:
d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)
where the first term on the right side is the derivative of the square root expression and the second term is the derivative of d with respect to time.
Now we need to find d in terms of t, given the maximum speeds of the car and the plane. Let's assume that they both start at time t = 0 and are racing for a time of T. Then, we can write:
d = 200T (distance traveled by the car)
d + 70 = 300T (distance traveled by the plane)
Solving for T, we get:
T = 70/100 = 0.7 hours = 42 minutes
Substituting T back into the expressions for d, we get:
d = 200(0.7) = 140 km
d + 70 = 300(0.7) = 210 km
Now we can substitute these values into the expression for the rate of change of the distance between the car and the plane:
d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)
d(distance)/dt = (1/2)[tex](140^{2} +500^{2} )^{(-1/2)}[/tex] * (2*140/60)(300 - 200)
d(distance)/dt = -63.63 m/s
Therefore, the rate of change of the distance between the car and the plane when both are at maximum speed and the plane is ahead by 70m is approximately -63.63 m/s. Note that the negative sign indicates that the distance between them is decreasing, since the plane is ahead of the car.
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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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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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You want to determine what percentage of working adults in your neighborhood regularly ride the bus to work. Which sampling method and survey question ar
best?
OA. Wait at the bus stop one morning and ask all working adults, "How many times per week do you ride the bus to work?"
O B. Go to every fifth house and ask the working adults, "How many times per week do you ride the bus to work?"
O C. Leave a note at each house asking working adults to call and answer the question, "Do you ever ride the bus to work?"
OD. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"
To determine what percentage of working adults in your neighborhood regularly ride the bus to work, the best sampling method and survey question are D. Enter the names of all adults in your neighborhood into a computer program to randomly select a sample and ask, "Do you ever ride the bus to work?"
What is the best sampling method?The best sampling method involves random sampling of the population.
A random sample gives each member of the population an equal chance of being selected as a participant in the survey.
It is also described as a probability sampling method.
Thus, in this instance, the correct option is D.
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Zayn and Attia are thinking of a number each. What is Attia's number? My number is greater than 2. 12 and 20 are multiples of my number. My number is the 11th multiple of Zayn's number.
Answer:
Me: 60
Zayn and Attia: 6
Step-by-step explanation:
12 = 2 × 2 × 3
20 = 2 × 2 × 5
LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60
My number is 60.
Zayn's and Attia's numbers are 6.
Simplify sqrt(27) \cdot sqrt(12) \cdot sqrt(147)
Answer:
Step-by-step explanation:
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).
The diameter of a circle is 9cm. Find its area to the nearest whole number
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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Find the union of each of the following pairs of sets A={2,4,6,8} and B={1,2,3}
Answer:
The union of sets A and B is:
A U B = {1, 2, 3, 4, 6, 8}
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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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]
Find x and y in terms of a and b.
Sax + by = 0
x + y = 2
(x, y) =
(a + b)
I don't know how to do.
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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Triangle ABC is given with coordinates A(-8, -8), B(-8, -2), C(-4, -2).
The ordered pair (2,y) is on line AC. Enter the value of y for this ordered pair.
The value of y for this ordered pair is 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of line AC;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 8)/(-4 + 8)
Slope (m) = 6/4
Slope (m) = 3/2
At data point (-4, -2) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 2 = 3/2(x + 4)
y = 3x/2 + 4
When x = 2, the y-value is given by;
y = 3(2)/2 + 4
y = 7.
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I need help? I’m not sure what to do in this equation?
The measure of angle C is given as follows:
m < C = 44º.
How to obtain the measure of angle C?To obtain the measures of the angles in this problem, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.
Considering that the sum of the measures of the internal angles of a triangle is of 180º, and angles C, D and E, the value of x is obtained as follows:
4x - 16 + 6x - 1 + 4x - 13 = 180
14x - 30 = 180
14x = 210
x = 210/14
x = 15.
Hence the measure of angle C is obtained as follows:
m < C = 4 x 15 - 16 = 44º.
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A square pyramid has a base measuring 10 inches on each side. The height of the pyramid is 5 inches.
A similar square pyramid has a base measuring 2 inches on each side.
How do the surface areas of these pyramids compare?
The surface area of the larger pyramid is Response area times the surface area of the smaller pyramid.
The surface area of the larger pyramid in discuss would be 25 times the surface area of the smaller pyramid.
How did the surface areas of the pyramids compare?It follows from the task content that the surface area of the larger pyramid and the smaller pyramid are to be compared.
By observation; the differing dimensions are such that the ratio of the larger pyramid to the smaller pyramid is; 10 / 2 = 5.
On this note, the ratio of the area of the pyramids are such that the larger pyramid is 5² = 25 times larger than that of the smaller pyramid.
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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
Justin makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
Question 10 (10 points)
You have this great idea for a business, but need to write at
least a 50 page business proposal to hand out to potential
investors. As of today, you have 15 pages done. How many
pages do you have left to write?
Inequality:
+p>
Solution: p>
Blank 1:
Blank 2:
Blank 3:
Answer:
p≥35
Step-by-step explanation:
because you have done 15 so you subtract 15 from 50 giving you 35 and then you would say p is greater than or equal to 35 cause 50 pages is your minimum
Solve for x.
x+6= √2x+29 +9
The solution to the equation is x = 10 or x = -2.
What is an equation?An equation refers to a mathematical expression showing that two expressions are equal.
It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).
To solve for x, we shall start with the given equation:
x + 6 = √(2x + 29) + 9
Subtract 9 from both sides:
x - 3 = √(2x + 29)
Square both sides:
[tex](x - 3)^2[/tex] = 2x + 29
Expand the left side:
[tex]x^2[/tex] - 6x + 9 = 2x + 29
We then subtract 2x and 9 from both sides:
[tex]x^2[/tex] - 8x - 20 = 0
Next, actor the quadratic equation:
(x - 10)(x + 2) = 0
Therefore, the equation x = 10 or x = -2
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The product of two negative integers is a negative integer.
Answer:
False. The product of two negative integers is a positive integer.
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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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.
Ming is paid an hourly rate. One week he earned $157.50 by working 30 hours per week. If he works 35 hours the next week, how much will he earn?
What is the next number in the following series: 101, 001, 66, ______?
The next number in the series would be 31 so the complete series is 101, 001, 66, 31.
How to find the next number ?The first thing we observe is that 101 equals 100 plus one. The second term, 001, equals 0 plus 1. Now consider the distinctions between consecutive terms:
101 - 001 = 100
001 - 66 = -65
When we look at the disparities (100, -65), we can see a pattern. The difference between 100 and 65 is a factor of 35. We can now apply this distinction to the final term in the series:
66 - 35 = 31
So the next number in the series is 31, completing the sequence: 101, 001, 66, 31.
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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
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%)
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.