Answer: -3/2
Step-by-step explanation:
FIrst rearrange the equation in y = mx + b form.
4x - 6y = -24
-6y = -4x - 24
y = 2/3x + 4
If the line is perpendicular, the slope must be the negative reciprocal of the current line.
The negative reciprocal of 2/3 is -3/2.
Samir bought three pounds of strawberries for $12.00. What is the price, in dollars
per ounce of strawberries?
1 pound = 16 ounces
Before you try that problem, answer the question below.
How many ounces of strawberries did Samir buy?
Kingsley knows that 1inch is about 2.45 centimeters. He wants to write an equation he can use to convert any given length in inches (i) to centimeters (c)
How should Kingsley write his equation?
A.) c/i = 2.54
B.) c = 2.54i
C.) i = c/2.54
Since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
What is equation ?
An equation is a statement that asserts the equality of two expressions, usually separated by an equals sign (=). The expressions on either side of the equals sign may contain one or more variables, which are unknown values that can be determined by solving the equation.
Kingsley wants to convert a given length in inches to centimeters. He knows that 1 inch is about 2.45 centimeters.
Let's call the length in inches "i" and the length in centimeters "c".
We want to find an equation that relates i and c. We know that 1 inch is about 2.45 centimeters, so we can write:
1 inch = 2.45 centimeters
To convert from inches to centimeters, we can multiply the length in inches by 2.45. So:
c = 2.45i
This is the equation Kingsley can use to convert any given length in inches to centimeters.
Alternatively, we can rearrange this equation to solve for i:
c = 2.45i
Divide both sides by 2.45:
c/2.45 = i
So the equation for converting from centimeters to inches is:
i = c/2.45
Therefore, since Kingsley wanted an equation to convert from inches to centimeters, the correct answer is B) c = 2.54i.
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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:
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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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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59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer
The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).
The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].
We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].
This is a infinite geometric series with first term a = -5x and common ration r = -5x.
It is convergent when
|r| < 1
|-5x| < 1
|-5| |x| < 1
5|x| < 1
Divide by 5 on both side, we get
|x| < 1/5
The series is convergent when x ∈ (-1/5, 1/5).
Sum of the series is
Sₙ = a/1 - n
Sₙ = (-5x)/{1 - (-5x)}
Sₙ = (-5x)/(1 + 5x)
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The complete question is:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]
Create a trigonometric function that models the ocean tide..
Explain why you chose your function type. Show work for any values not already outlined above.
Answer:
One possible function that models the ocean tide is:
h(t) = A sin(ωt + φ) + B
where:
h(t) represents the height of the tide (in meters) at time t (in hours)
A is the amplitude of the tide (in meters)
ω is the angular frequency of the tide (in radians per hour)
φ is the phase shift of the tide (in radians)
B is the mean sea level (in meters)
This function is a sinusoidal function, which is a common type of function used to model periodic phenomena. The sine function has a natural connection to circles and periodic motion, making it a good choice for modeling the regular rise and fall of ocean tides.
The amplitude A represents the maximum height of the tide above the mean sea level, while B represents the mean sea level. The angular frequency ω determines the rate at which the tide oscillates, with one full cycle (i.e., a high tide and a low tide) occurring every 12 hours. The phase shift φ determines the starting point of the tide cycle, with a value of zero indicating that the tide is at its highest point at time t=0.
To determine specific values for A, ω, φ, and B, we would need to gather data on the tide height at various times and locations. However, typical values for these parameters might be:
1. A = 2 meters (representing a relatively large tidal range)
2. ω = π/6 radians per hour (corresponding to a 12-hour period)
3. φ = 0 radians (assuming that high tide occurs at t=0)
4. B = 0 meters (assuming a mean sea level of zero)
Using these values, we can write the equation for the tide as:
h(t) = 2 sin(π/6 t)
We can evaluate this equation for various values of t to get the height of the tide at different times. For example, at t=0 (the start of the cycle), we have:
h(0) = 2 sin(0) = 0
indicating that the tide is at its lowest point. At t=6 (halfway through the cycle), we have:
h(6) = 2 sin(π/2) = 2
indicating that the tide is at its highest point. We can also graph the function to visualize the rise and fall of the tide over time:
Tide Graph
Overall, this function provides a simple and effective way to model the ocean tide using trigonometric functions.
(please mark my answer as brainliest)
Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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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
which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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The dot plots below show the number of students in attendance each day in Mr. Wilson's class and Mr. Watson's class in April. What is the difference of the medians as a multiple of the interquartile range? A. B. C. D.
The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.
What is median?The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.
For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.
We can first find the medians and interquartile ranges of the two dot plots.
For Mr. Wilson's class:
Median = 12
Q1 = 10
Q3 = 14
IQR = Q3 - Q1 = 14 - 10 = 4
For Mr. Watson's class:
Median = 10
Q1 = 8
Q3 = 12
IQR = Q3 - Q1 = 12 - 8 = 4
The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:
$$\frac{2}{4} = \boxed{0.5}$$
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Construct triangle PQR in which angle Q = 30 deg , angle R=60^ and PQ + QR + RP = 10cm
We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm, here is a guide:
Draw a line segment AB = 10 cm.Construct angle 30° at point A and angle 60° at point B.Draw angle bisectors to angles A and B.Make sure these angle bisectors intersect at point P.Draw perpendicular bisector to line segment AP.Let this bisector meet AB at Q.Then draw perpendicular bisector to line segment BP.Let this bisector meet AB at R.Join PQ and PR.PQR is the required triangle.What is a triangle?A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.
Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.
Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.
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Help i need this question solved
Answer: D. Square
Step-by-step explanation:
The shape created by the cross section of the cut through a square pyramid is a square.
To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.
The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.
complete the table below.
4775 g968r648 747474874 483892874 23773259635y84b2375789325 7437594365825 4378574937587 49388959365n 98437858746587 32o4iy548569
Answer:
?
Step-by-step explanation:
Which expressions are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1
Answer:
8(3/4y - 2) + 6(-1/2x + 4) + 1 can be simplified as:
6(-1/2x) = -3x
8(3/4y) = 6y
8(-2) = -16
6(4) = 24
1 remains as 1.
So the expression becomes:
6y - 3x - 16 + 24 + 1
which simplifies to:
6y - 3x + 9
Therefore, the expressions that are equivalent to 8(3/4y - 2) + 6(-1/2x + 4) + 1 are:
6y - 3x + 9
Mrs. Cabana has 8 pets total. Three of the pets are chameleons and the rest are fish. Select all the answers that are a ratio relationship for Mrs. Cabana's pets.
Question 1 options:
Multi choice
3/5
3 to 11
3:8
5 to 8
8:1
Answer: numbers 1,3 and 4
Step-by-step explanation:
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 0.59°C and 0.88°C.
The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.
What is mean?The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.
In this question, using the formula,
z-score = (x – μ) / σ
where:
x: individual data value
μ: population mean
σ: population standard deviation
for x=0.59
μ= 0
σ= 1
z-score= 0.59
Probability=0.7224
for x=0.88
z-score= 0.88
Probability=0.8106
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Write a sine function that has a midline of, y=5, an amplitude of 4 and a period of 2.
Answer:
y = 4 sin(π x) + 5
Step-by-step explanation:
A sine function with a midline of y=5, an amplitude of 4, and a period of 2 can be written in the following form:
y = A sin(2π/ x) +
where A is the amplitude, is the period, is the vertical shift (midline), and x is the independent variable (usually time).
Substituting the given values, we get:
y = 4 sin(2π/2 x) + 5
Simplifying this expression, we get:
y = 4 sin(π x) + 5
Therefore, the sine function with the desired characteristics is:
y = 4 sin(π x) + 5
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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P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
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!
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
select a random integer from -200 to 200. which of the following pairs of events re mutualyle exclusive
The pairs of events of random integers are pairs of events are,
even and odd , negative and positive integers, zero and non-zero integers.
Two events are mutually exclusive if they cannot occur at the same time.
Selecting a random integer from -200 to 200,
Any two events that involve selecting a specific integer are mutually exclusive.
For example,
The events selecting the integer -100
And selecting the integer 50 are mutually exclusive
As they cannot both occur at the same time.
Any pair of events that involve selecting a specific integer are mutually exclusive.
Here are a few examples,
Selecting an even integer and selecting an odd integer.
Selecting a negative integer and selecting a positive integer
Selecting the integer 0 and selecting an integer that is not 0.
But,
Events such as selecting an even integer and selecting an integer between -100 and 100 are not mutually exclusive.
As there are even integers between -100 and 100.
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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
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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given natural numbers a and b not both equal to 0, we know that there exist integers k and l with ak bl
The equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l).
The equation ak + bl = 0 is a linear equation in two variables and is solved using the method of elimination. The equation can be written in the form ax + by = c, where a, b, c are constants. To solve this equation, both sides of the equation should be divided by the coefficient of one of the variables (a or b). This will result in a equation of the form x + qy = r, where q and r are constants. Then, the equation can be rearranged to the form y = -qx + r. This is the equation of a straight line, which can be graphed. The point of intersection of the two lines, ak + bl = 0 and y = -qx + r, is the solution for the two variables (k and l). The two variables can then be calculated using the point of intersection by substituting the x and y values into the two equations. In this way, the two variables k and l can be found such that ak + bl = 0.
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What are the integers k and l such that ak + bl = 0?
On the day a video was posted online, 5 people watched the video. The next day the number of viewers had doubled. Assume the
number of viewers continues to double each day.
1. On which day will 640 people see the video? Explain or show your reasoning.
2. What strategy would you use to find the first day when more than 20,000 people will see the video (if the trend continues)?
On the 7th day after the videο was pοsted, 640 peοple will see the videο.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data.
1 Let's start by finding the pattern in the number οf viewers. We knοw that οn the first day, 5 peοple watched the videο. On the next day, the number οf viewers dοubled tο 5 x 2 = 10. On the third day, the number οf viewers dοubled again tο 10 x 2 = 20. We can see that the number οf viewers is dοubling each day, which means we can write the number οf viewers as:
[tex]V = 5 x 2^n[/tex]
where n is the number οf days after the videο was pοsted.
Nοw we want tο find οn which day the number οf viewers will be 640. Sο we can set V equal tο 640 and sοlve fοr n:
[tex]640 = 5 x 2^n[/tex]
[tex]2^n = 128[/tex]
n = lοg2(128) = 7
2. Tο find the first day when mοre than 20,000 peοple will see the videο, we can set V equal tο 20,000 and sοlve fοr n:
[tex]20,000 = 5 x 2^n[/tex]
2^n = 4,000
n = lοg2(4,000) ≈ 11.29
Since n represents the number οf days after the videο was pοsted, we can rοund up tο the next whοle number tο find the first day when mοre than 20,000 peοple will see the videο. Therefοre, οn the 12th day after the videο was pοsted, mοre than 20,000 peοple will see the videο if the trend cοntinues
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The following joint probability density function for the random variables Y1 and Y2, which represent the proportions of two components in a somaple from a mixture of insecticide.
f(y1,y2) = { 2, 0 <= y1 <= 1, 0 <= y2 <= 1, 0 <= y1+y2 <=1
{ 0, elsewhere
For the chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample. Find E(Y1+Y2) and V(Y1+Y2).
The joint probability density function for the random variables Y1 and Y2 E(Y1+Y2) and V(Y1+Y2) is 41/144.
To find E(Y1+Y2), we need to integrate the sum of Y1 and Y2 over their joint probability density function:
E(Y1+Y2) = ∫∫ (y1 + y2) f(y1,y2) dy1 dy2
= ∫∫ (y1 + y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 <=1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex](y1 + y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (2y1 + 1) (1-y1)² dy1
= 5/12
To find V(Y1+Y2), we can use the formula V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]².
First, we need to find E[(Y1+Y2)^2]:
E[(Y1+Y2)²] = ∫∫ (y1+y2)² f(y1,y2) dy1 dy2
= ∫∫ (y1² + y2² + 2y1y2) (2) dy1 dy2, where the limits of integration are 0 to 1 for both y1 and y2 and y1+y2 = 1
= ∫[tex]0^1[/tex] ∫[tex]0^{(1-y1)}[/tex] (y1² + y2² + 2y1y2) (2) dy2 dy1
= ∫[tex]0^1[/tex] (1/3)y1³ + (1/2)y1² + (1/2)y1
(1/3)y1 + (1/4) dy1
= 7/12
Next, we need to find [E(Y1+Y2)]²:
[E(Y1+Y2)]² = (5/12)² = 25/144
Therefore, V(Y1+Y2) = E[(Y1+Y2)²] - [E(Y1+Y2)]² = (7/12) - (25/144) = 41/144.
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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.
