A function is a relationship between inputs where each input is related to exactly one output.
The function with a decay rate of 5% is
f(x) = 100(0.95)
This is with a decay rate of 5%
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Decay rate = 5%
5% = 5/100 = 0.05
The total rate = 100%
100% = 100/100 = 1
The rate to multiply with the function.
= 1 - 0.05
= 0.95
A)
f(x) = 100(-5)
This is not a decay rate of 5%
B)
f(x) = 105(0.05)
This is with a decay rate of 95%.
C)
f(x) = 100(0.95)
This is with a decay rate of 5%
D)
f(x) = 100(1.05)
This is not a decay rate function.
E)
f(x) = 100(5)
This is not a decay rate function.
Thus,
The function with a decay rate of 5% is
f(x) = 100(0.95)
This is with a decay rate of 5%
Option C is the correct answer.
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if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl?
The probability that her third child would be a girl is 50%.
Probability:
In math probability means the possible of happening a particular event amount the total number of event.
Given,
Here we need to find if a woman's first child is a girl and her second child is also a girl, what is the probability that her third child would be a girl.
We already know that, there are two sex chromosomes X and Y.
And in the humans are diploid having two sex chromosomes, in females a pair of the X chromosome is found while in males an X and Y chromosome is present.
So, there is 50% chance that the subsequent child is going to be a girl because it entirely depends upon the chromosome of the sperm which fertilizes the ovum.
For each pregnancy features a 50% chance of leading to a boy or girl and this doesn't include the likelihood of multiples.
Here already having 2 girls previously doesn't affect the probabilities of any resulting pregnancy.
Therefore, the prospect of getting a girl remains at 50%.
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how do you calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity?
The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .
In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.
When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
The degrees of freedom in this case are calculated with the formula:
df=bins(or categories)−1−number of parameters of the distribution.
The degrees of freedom for the chi-square are calculated using the following formula:
df = (r-1)(c-1)
where r is the number of rows and c is the number of columns.
The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.
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determine the equation of the hyperbola with foci (13,-1)(13,−1) and (-13,-1)(−13,−1), and co-vertices (0,11)(0,11) and (0,-13)(0,−13).
The equation of the hyperbola is
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 3650 = 0[/tex]
What is a hyperbola?
In mathematics, a hyperbola is a conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the centre. It is a type of smooth curve lying in a plane and has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The standard form of writing an equation of the hyperbola is,
[tex]\frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
Where (h, k) is the centre; a is the distance from the centre to vertices; b is the distance from co-vertices to the centre.
Given,
Foci of the hyperbola are (13, -1); (-13, -1)
Co-vertices are (0,11); (0,-13)
As we know that the centre of the hyperbola is the midpoint of the foci, then it will be (h,k) = (0,-1)
Distance from centre to foci is, c = 13 [2c = 26; c = 26 / 2 = 13]
Distance from co vertices to foci is, b = 12 [ 2b = 24; c = 24 / 2 = 12]
let us assume a is the distance from the centre to the vertices.
we know that,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
then,
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]a = \sqrt{ {13}^{2} - {12}^{2} } [/tex]
[tex]a = \sqrt{169 - 144} [/tex]
[tex]a = \sqrt{25} [/tex]
[tex]a = 5[/tex]
Now, the equation of the hyperbola is,
[tex] \frac{ {(x - h)}^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[tex] \frac{ {(x - 0)}^{2} }{ {5}^{2} } - \frac{ {(y + 1})^{2} }{ {12}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{25} - \frac{ {y}^{2} + 2y + 1 }{144} = 1[/tex]
[tex] \frac{144 {x}^{2} - 25 {y}^{2} - 50y - 50 }{25 \times 144} = 1[/tex]
[tex]144 {x}^{2} - 25 {y}^{2} - 50y - 50 = 25 \times 144[/tex]
Hence the required equation is,
[tex]144 {x}^{2} - 25 {y}^{2} - 3650 = 0[/tex]
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What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di).
The correct option D)c = –3, d = –2; for which the expression becomes real number.
Explain the term real number?In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In opposed to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in evaluations of continuously altering quantities including size and time.For the given question,
The expression is-
= i(2 + 3i)(c + di)
Simplifying,
= i(2c + 2di + 3ci + 3d²)
= 2ci + 2di² + 3ci² + 3di³
= 2ci - 2d -3c - 3di
= (2c - 3di)i - 2d - 3c
Now, again for expression to produce a real number, the coefficient of must be zero.
Let's evaluate each choice.
A: 2c - 3d = 2x2 -3x3 = -5
B: 2x(-2) - 3x3 = -13
C: 2x3 - 3x(-2) = -12
D: 2x(-3) - 3x(-2) = 0
As option D only has the positive number, thus define the expression.
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The complete question is-
What values of c and d would make the following expression represent a real number? i(2 + 3i)(c + di)
choices: A)c = 2, d = 3 B)c = –2, d = 3 C)c = 3, d = –2 D)c = –3, d = –2
Answer: D) c = –3, d = –2
Step-by-step explanation:
Correct on Edge
which of the following would be a correct interpretation of a 99% confidence interval such as 4.15.6? question content area bottom part 1 choose the correct answer below. a. it means that 99% of sample means fall between 4.1 and 5.6. b. we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of . c. there is a 99% chance that will fall between 4.1 and 5.6. d. it means that 99% of a
We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.
The probability that it contains the true population mean is 99%.
Given 99% confidence interval : 4.1 < μ < 5.6
Then, the correct interpretation is we are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
Hence the answer is We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.
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show intro/instructions chance is skiing on a circular ski trail that has a radius of 0.9 km. chance starts at the 3-o'clock position and travels 2.75 km in the counter-clockwise direction. how many radians does chance sweep out? radians how many degrees does chance sweep out? degrees when chance stops skiing, how many km is chance to the right of the center of the ski trail? km when chance stops skiing, how many km is chance above the center of the ski trail?
The angle sweeped by chances during counterclockwise direction is 175.15° and in radian is 3.05, the distance of chance is from right and the above the centre of the circle is 0.27 km and 0.261km respectively.
Chance is running on a circular track that has a radius 0.9 km and he goes 2.75km into the counter clockwise direction from the 3-o'clock position.
The arc length of the circle is given by,
L = 2πR(A/360)
R is the radius,
L is the length of the arc,
A is the angle made in degrees.
Putting values,
2.75 =2π(0.9)(A/360)
A = 175.15°C.
Now, converting it into radians,
A in radian is 3.05.
Distance D of chance to the right of centre of the ski trail is,
D = R(1-0.7)
D = R(0.3)
D = 0.27 Km.
The distance D' of chance above the centre of the ski trail is,
D' = R(1-0.71)
D' = R(0.29)
D' = 0.261 Km.
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Which represents a side length of a square that has an area of 450 square inches?15 startroot 2 endroot inches in. 16 startroot 3 endroot inches in. 112. 5 in. 115. 5 in.
Using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².
What is the area?A shape's area can be calculated by contrasting it with squares of a known size.
The square meter (abbreviated as m2), which is the area of a square whose sides are one meter long, is the common unit of area in the International System of Units (SI).
Three such squares would be the same size as a form with a three-square-meter area.
The area of any other shape or surface is a dimensionless real number, and the unit square is defined in mathematics to have area one.
So, the area of the square:
A = b²
Where B is the square's long side.
A = 450in²
A = b²
b² = 450
b = √450
b = 15√2 in
Therefore, using the area formula of the square we know that (A) 15√2 in inches represents a side length of a square that has an area of 450in².
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Correct question:
Which represents a side length of a square that has an area of 450 square inches?
a. 15 start root 2 end root inches in.
b. 16 start root 3 end root inches in.
c. 112. 5 in.
d. 115. 5 in.
In a statistical test of hypotheses, we say the data are statistically significant at level α if.
If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
What is hypotheses ?An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.
One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.
It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.
Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
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Please help me solve this one.
Thank u!
Answer:
20 cm²
Step-by-step explanation:
It is a right triangle.
So, using Pythagorean theorem: OS² = OR² - RS²
OR = r (radius) + 8
OS = r
RS = 16
=> r² = (r+8)² - 16²
r² = r² + 16r + 64 - 256
r² = r² + 16r - 192
16r = 192
r = 192 / 16 = 12cm²
a) 12 cm²
b) 12 + 8 = 20 cm²
Please help!!! Needs done by tomorrow
The population of the small town in 2025 is 22234
How to determine the population in 2025?The given parameters in the question are
Initial population =24597Rate of decay = 2%These parameters can be represented as
a = 24597
r = 2%
The equation of the function can be represented as
P(t) = a(1 - r)^t
So, we have
P(t) = 24597 * (1 - 2%)^t
In 2025, we have
Year = 2025
This means that
t = 2025 - 2020
So, we have
t = 5
Substitute t = 5 in P(t) = 24597 * (1 - 2%)^t
P(5) = 24597 * (1 - 2%)^5
Evaluate the expression
P(5) = 22234
Hence, the population is 22234
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a rectangular block of mass m has dimensions as shown. in terms of m, a, b and c, find the rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces. b. let m
The rotational inertia of the block about an axis of rotation through one of the corners of the block which is perpendicular to the large faces will be M(a²+b²)/3.
What is rotational inertia?Any item that can be rotated has the property of rotational inertia. It is a scalar value that indicates how challenging it is to alter an object's rotational velocity around a certain rotational axis. The role of mass in linear mechanics is analogous to that of rotational inertia in rotational mechanics. Because it measures moment of inertia as it is rotating, this property is also known as rotational inertia. A measurement of an object's resistance to changes in its angular velocity is called rotational inertia. Imagine turning an item with a specific torque. As the torque is being applied, measure the angular acceleration. The rotational inertia of the item increases as the resultant angular acceleration decreases.
Here,
The major calculations are attached in image.
Moment of Inertia of plate passing through O is I = Ma²/12
and, ly = Mb²/12
by perpendicular axis theorem I2 = Ma²/12+Mb²/12
The distance of edge and the center is d = √(a²+b²)/4
So by parallel axis theorem, IA = Ma²/12+ Mb²/12 + Md² = M(a²+b²)/3
M(a²+b²)/3 is the rotational inertia of the block about a rotating axis passing through one of its corners and perpendicular to its large faces.
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This graph shows the different gang-related activities reported in small and large communities.
A graph titled Report of Gang Related Criminal Activity shows activities on the horizontal axis and percentage of people reporting on the vertical axis. 15% reported aggravated assault. 10% reported burglary. 23% reported drug sales. 47% reported graffiti. 8% reported larceny/theft. 6% reported motor vehicle theft. 5% reported robbery.
According to the graph, which gang-related activity is least reported in a large community?
graffiti
robbery
drug sales
aggravated assault
Mark this and return
Based on the graph showing the different gang-related activities reported in small and large communities, a gang-related activity which is least reported in a large community is: B. robbery.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.
Additionally, a pie chart is generally considered as the best graph to be used in graphically representing percentages and relative proportions.
According to the graph, we can logically deduce the following percentages of people that reported the different gang-related activities in small and large communities;
Aggravated assault = 15%.Burglary = 10%. Drug sales = 23% Graffiti = 47% Larceny/theft = 8% Motor vehicle theft = 6%Robbery = 5%In conclusion, robbery is the least reported gang-related activity in a large community with a percentage of 5 percent (5%).
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• we have two concentric circles. a chord of the larger circle is tangent to the smaller circle and has length 8. what’s the area of the annulus–the region between the two circles?
The Area of annulus - the region between the two circle is 50.26cm²
According to the question,
The length of chord of the large circle which is tangent to the small circle : AB = 8cm
Le the radius of large circle "R" and radius of smaller circle "r"
AB is a tangent to the smaller circle
AM = 8/2
=> AM = 4cm
In ΔOAM,
Using Pythagoras theorem ,
OA² = OM² + AM²
=> R² = r² + (4)²
=> R² - r² = 16
So, the area of annulus = π(R² - r²)
=> 16π (putting π = 3.14)
=> 50.26cm² is required area
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Kaitlynn needs 3 pounds of fruit for a salad.
She already has 3/4 pounds of apples and 1/3 pounds of grapes.
How many more pounds of fruit does she need to buy?
answer:
1.92 pounds or 23/12 lb
step-by-step explanation:
first convert 3/4 and 1/3 to fractions that have the same denominator such as 9/12 and 4/12. then add the two numbers together and subtract it by 3 to get the answer. hope that helps!
what is a simpler form for the equation ^4√2401x^12y^16
Simplified form of fourth root of 2401x¹²y¹⁶ is 7x³y⁴
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Given,
⁴√2401 x¹² y¹⁶=⁴√7*7*7*7 (x³)⁴(y⁴)⁴
=⁴√(7)⁴ (x³)⁴(y⁴)⁴
=⁴√(7 x³y⁴)⁴
= 7 x³y⁴
Therefore, Simplified form fourth root of 2401x¹²y¹⁶ is 7x³y⁴.
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write the general antiderivative. (use c for the constant of integration. remember to use absolute values where appropriate.) 1 8 x 1 8x 1 8 x dx
The integration of the given function is as follows.
What is anti derivative?
In calculus, an antiderivative, inverse derivative, primitive perform, primitive integral or integral of a perform f could be a differentiable perform F whose spinoff is adequate to the initial perform f. this could be explicit symbolically as F' = f
Main body:
f (x) = x/8 +1/8x + (1/8)^x
to find the anti derivative , we need to integrate the function;
apply sum rule:
[tex]\int\ f{(x)} + g (x)\, dx[/tex] = [tex]\int\ f {(x)} \, dx + \int\ g {(x)} \, dx[/tex]
[tex]\int\ {(x/8)} \, dx[/tex] = x² /16
[tex]\int\ f {(1/8x)} \, dx[/tex] = 1/8 ln|x|
[tex]\int\ f {(1/8^x)} \, dx[/tex] = [tex]-\frac{1}{3\ln \left(2\right)\cdot \:8^x}[/tex]
hence
[tex]\int \frac{x}{8}+\frac{1}{8x}+\frac{1}{8^x}dx[/tex]= [tex]\frac{x^2}{16}+\frac{1}{8}\ln \left|x\right|-\frac{1}{3\ln \left(2\right)\cdot \:8^x}+C[/tex]
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An online tutoring company charges $25 per session plus an annual membership fee of $45. If a member is charged $545 for the year, how many sessions did they have that year?
The total number of sessions they did in that year will be equal to 20.
What is an equation?Equations are mathematical expressions with two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be similar to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a simple fundamental equation.
As per the data given in the question,
The charge per session = $25
Annual membership charge = $45
Total money paid = $545
Money left after paying for the annual membership = $545 - $45= $500
The total number of sessions in $500 will be,
T = 500/25
T = 20 sessions.
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A circle with radius of 2 cm sits inside a 7 cm x 11 cm rectangle
I believe the answer you seek would be that the area of the shaded region would be [tex]64.43 cm^2[/tex].
Hope this helps!
sketch the nyquist plot based on the bode plots for each of the following systems , and then compare your results whit that obtained by using the matlab command nyquist : dont be concerned with the details of exactly where the curve goes , but do make sure it crosses the real axis at the right spot , has the correct number of -1 encirclements and goes off to infinity in the correct direction. A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D). Usinng your plots , estimate the range of k for which each system is stable , and qualitatively verif your result by using a rough sketch of a root locus plot.
Sketching the nyquist plot based on the bode plots for the mentioned systems require a certain understanding of bode plots explained in detail.
What do you understand by bode plots?In reality, Bode plots are a collection of graphs that display a system's frequency response. This system might be any system (not simply a circuit!) that changes its behavior when its frequency (cycles per second) changes.
Frequency Response simply describes how our system will alter in response to a specific input frequency. This collection of notes will be referred to as our input frequency.
Bode charts often have two graphs. We'll refer to one as the magnitude plot and the other as the phase angle plot.
We'll need something initially called a transfer function. Typically represented as H(s) or H(j). A transfer function often equates to the ratio of the output to the input.
A). >KG ( s) a= K( s+2 ) / s + 10 B.>KG ( s) = K / ( s + 10 )(s+2)2 C).>KG ( s) = K (s+10)(s+10) / (s+100)(s+2)3 D)
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a right triangle has legs measuring 20 inches and 21 inches. what is the length of the hypotenuse, in inches?
Answer: 29 inches.
Step-by-step explanation:
The formula to find the hypotenuse is a^2 + b^2 = c^2.
20^2= 400, and 21^2=441. Together, it was 841. Square root that, and your answer is 29.
-
a^2 + b^2 = c^2
20^2 + 21^2 = c^2
400 + 441= c^2
881 = c^2
29=29
ways 3 people can divide a 10 segment into a equal amount of shares
The number of ways to divide the shares into 10 equal segments is 120
How to determine the to divide the shares into equal segments?from the question, we have the following parameters that can be used in our computation:
Total number of segments, n = 10
Numbers to people, r = 3
The number of ways of dividing the segment is then calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 10 and r = 3
Substitute the known values in the above equation, so, we have the following representation
Total = ¹⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have the following representation
Total = 10!/7!3!
Evaluate the quotient
Total = 120
Hence, the number of ways is 120
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which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
The correct statement to represent the comparison between defective parts produced by machines is option d. Machine A usually, but not always, produced fewer defective parts than machine B.
As given in the question,
Number of machines in a factory = 2
Statement compares the :
Number of defective parts produced by machines during first 4 hours
for 19 days.
Observations from the given scatterplot are:
a. Machine A always produced the same number of defective parts as machine B.
False. Variation in producing number of defective parts.
b. Machine A always produced fewer defective parts than machine B.
False.
c. Machine A always produced more defective parts than machine B.
False.
d. Machine A usually, but not always, produced fewer defective parts than machine B.
True. Sometimes like when Machine A produce 7 defective parts machine B produce 5.
e. Machine A usually, but not always, produced more defective parts than machine B.
False.
Therefore, option d) Machine A usually, but not always, produced fewer defective parts than machine B is the correct answer.
The complete question is:
A factory has two machines, A and B, making the same part for refrigerators. The number of defective parts produced by each machine during the first hour of operation was recorded on 19 randomly selected days. The scatterplot below shows the number of defective parts produced by each machine on the selected days.
Which statement gives the best comparison between the number of defective parts produced by the machines during the first hour of operation on the 19 days?
a. Machine A always produced the same number of defective parts as machine B.
b. Machine A always produced fewer defective parts than machine B.
c. Machine A always produced more defective parts than machine B.
d. Machine A usually, but not always, produced fewer defective parts than machine B.
e. Machine A usually, but not always, produced more defective parts than machine B.
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A credit card company charges 10% interest at the end of every month on the outstanding balance of a credit card. Jacqueline’s last credit card bill was $250. For 3 months, she makes the minimum payment of $50 each month, and does not use the credit card. How much does she owe the credit card company at the end of 3 months?
She owe $167.25 of the credit card company at the end of 3 months.
What is simple interest?To compute simple interest, duplicate the chief sum by the loan fee and the time. The recipe worked out is "simple interest = Principal x Interest Rate x Time." This condition is the easiest approach to ascertaining interest.
According to question:We ave,
interest = 10%, loaned amount = $250, monthly payment = $50
Then,
interest of first month = $250×1×0.1 = $25
She makes a payment of $50
Then $250 - $50 + $25 = $225
Second month:
interest = $225 ×0.1 = $22.5
Payment of $50
remain loan = $225 - $50 + 22.5 = $197.5
And third month
interest = $197.5×0.1 = $19.75
payment of $50 Then
Net payable loan = $197.5 - $50 + $19.75 = $167.25
Thus, remaining loan amount is $167.25.
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Ignoring resistance, a sailboat starting from rest accelerates (dv/dt) at a rate proportional to the difference between the velocities of the wind and the boat. (a) The wind is blowing at 20 knots, and after 1 half-hour, the boat is moving at 10 knots. Write the velocity v as a function of time t. (b) Use the result of part (a) to write the distance traveled by the boat as a function of time.
V=Vw-ce^-kt is the velocity V as a function of time t when wind is blowing 20 knots and after 1 half hour the boat moves at 10 knots
What is acceleration?Acceleration is a vector quantity that is defined as the rate at which an object's velocity varies. When an object's velocity changes, it is said to be accelerating.
On occasion, sports broadcasters will suggest that a person is accelerating if they are traveling quickly. But speed has nothing to do with acceleration. Even while traveling very quickly, a person may not be accelerating. Changing the speed at which an item is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward. Throughout time, the velocity is shifting. Every second, the velocity is changing by a fixed amount of 10 m/s.
How to solve?
Based on the information from the exercise, we have the equation:
dt/dv=k(Vw−V)
where V is velocity of the boat in knots/hour, tt is time in hours, Vw is velocity of wind.
This equation can be written:
dv/dt = k(Vw -V)
dv/Vw-V =kdt
Now, the variables are separated, tt appears only on the right side, and v only on the left. Integrate the left side in relation to v, and the right side in relation to t:
dv/Vw-V =kdt
∫dv/Vw-V =∫kdt
let Vw -V = u
-dv=du
dv= -du
∫-du/u =k∫dt
-ln|u| =kt +C
-ln|Vw-V| = kt + C
V=Vw-ce^-kt
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the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound. what is the increase in percent
The increase in the price of the bananas = 8%
We know that the formula for percent change:
percent change = [(new value - old value)/ old value ] * 100
Here, the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound.
old value = 75 cents per pound
new value = 81 cents per pound
So, the percent increase in the price of bananas would be,
percent increase in price = [(81 - 75)/ 75 ] * 100
percent change = (6/75) * 100
percent change = 8%
Therefore, the increase is 8%
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Factoring trinomials 8x^2 + 2x -3
Answer:
(2x - 1) (4x + 3)
Step-by-step explanation:
During a certain period of time, 2,000 penguins had an annual growth rate of 19%. What will the population of penguins be after 5 years?
Use the Distributive Property to write an expression equivalent to 0.4(-5-7y-13.8).
Answer:
-2.8y-7.52
Step-by-step explanation:
multiply 0.4 by each of the numbers in the parentheses then simplify
Answer: -2.8y-7.52
Step-by-step explanation:
a circle has a radius of 8 what is its circumference do not round
Please help me!
Answer:
C = 50.27
Step-by-step explanation:
Hope this helps!
Answer:
C = 16 pi
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi * r
C = 2 * pi * 8
C = 16 pi
Find the radius of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 12.
A right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.
What is a right circular cylinder?The right circular cylinder is a cylinder with circular bases that are parallel to one another.
Three dimensions make up its form.
The two bases of the cylinder are joined at their centers by the cylinder's axis.
Sphere:
A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.
The radius of the right circular cylinder will be:
The formula for the volume of a sphere: V = 4/3πr²
Now, substitute r = 12 as shown:
V = 4/3πr²
V = 4/3π12²
V = 4/3π144
V = 7238.22947
Rounding off: 7238 units³
Nw, the formula for the volume of a right circular cylinder:
V = πr²h
Substitute V = 7238 and calculate for r as follows:
V = πr²h
7238 = πr²h
r² = 7238/πh
r = √7238/πh
Therefore, a right circular cylinder with the largest volume that can fit inside a sphere with a radius of 12 has a radius of √7238/πh units.
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