The Second Linearly Independent solution of the differential equation is:
y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)
When solving a second-order linear differential equation of the form
x²y'' - 42y = 0, it is important to find two linearly independent solutions to fully describe the general solution. The first solution is given as y₁=x⁷.
To find the second linearly independent solution, we can use the method of reduction of order.
Let y₂ = u(x)y₁(x), where u(x) is a function to be determined.
Then we have y₂' = u(x)y₁'(x) + u'(x)y₁(x) and y₂'' = u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x).
Substituting y₂ and its derivatives into the original differential equation, we have:
x²(u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x)) - 42u(x)y₁(x) = 0
Dividing by x²y₁(x), we get:
u''(x)/u(x) + 2/x[u'(x)/u(x)] - 42/x² = 0
Let v(x) = u'(x)/u(x), then v'(x) = u''(x)/u(x) - (u'(x))²/(u(x))². Substituting v(x) into the above equation, we have:
v'(x) + 2/xv(x) - 42/x² = 0
This is now a first-order linear differential equation that can be solved using an integrating factor. Letting mu(x) = x², we have:
(x²v(x))' = 42
Solving for v(x), we get:
v(x) = 21/x + C/x²
where C is an arbitrary constant. Substituting back to u(x), we get:
u(x) = Ax³ + Bx⁻⁻¹⁸
where A and B are constants. Therefore, the second linearly independent solution is
y₂ = (Ax³ + Bx⁻¹⁸)x⁷ = Ax¹⁰ + Bx⁻¹¹
Hence, the general solution of the differential equation is:
y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)
where c₁ and c₂ are arbitrary constants
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NO LINKS!!! URGENT HELP PLEASE!!!
Solve ΔABC using the Law of Sines
1. A = 29°, C = 63°, c = 24
2. A = 72°, B= 35°, c = 21
Answer:
1) B = 88°, a = 13.1, b = 26.9
2) C = 73°, a = 20.9, b = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Question 1Given values:
A = 29°C = 63°c = 24As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies B=180^{\circ}-A-C[/tex]
[tex]\implies B=180^{\circ}-29^{\circ}-63^{\circ}[/tex]
[tex]\implies B=88^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies a=13.0876493...[/tex]
[tex]\implies a=13.1[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}[/tex]
[tex]\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies b=26.9194211...[/tex]
[tex]\implies b=26.9[/tex]
[tex]\hrulefill[/tex]
Question 2Given values:
A = 72°B = 35°c = 21As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-72^{\circ}-35^{\circ}[/tex]
[tex]\implies C=73^{\circ}[/tex]
Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
Solve for a:
[tex]\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies a=20.8847511...[/tex]
[tex]\implies a=20.9[/tex]
Solve for b:
[tex]\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}[/tex]
[tex]\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}[/tex]
[tex]\implies b=12.5954671...[/tex]
[tex]\implies b=12.6[/tex]
Out of 1000 students who appeared in an examination,60% passed the examination.60% of the failing students failed in mathematics and 50% of the failing students failed in English.If the students failed in English and Mathematics only, find the number of students who failed in both subjects.
The value of number of students who failed in both mathematics and English is 40.
Since, Given that;
60% of the 1000 students passed the examination,
Hence, we can calculate the number of students who passed the exam as follows:
60/100 x 1000 = 600
So, 600 students passed the examination.
Now, let's find the number of students who failed the examination.
Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:
40/100 x 1000 = 400
Of the 400 failing students, we know that 60% failed in mathematics.
So, the number of students who failed in mathematics is:
60/100 x 400 = 240
Similarly, we know that 50% of the failing students failed in English.
So, the number of students who failed in English is:
50/100 x 400 = 200
Now, we need to find the number of students who failed in both subjects.
We can use the formula:
Total = A + B - Both
Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.
Substituting the values we have, we get:
400 = 240 + 200 - Both
Solving for Both, we get:
Both = 240 + 200 - 400
Both = 40
Therefore, the number of students who failed in both mathematics and English is 40.
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1. The vertices of APQR are P(1, 3), Q(5, 4) and
R(5, 15). Find the length of the perpendicular
from Q to PR.
The distance of the perpendicular from Q to line PR is D = 2.2135 units
Given data ,
Let the triangle be represented as ΔPQR
Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)
And , the equation of line of PR is given by
Slope m = ( 15 - 3 ) / ( 5 - 1 )
m = 3
y - 3 = 3 ( x - 1 )
Adding 3 on both sides , we get
y = 3x
y - 3x = 0
And , the point is Q(5, 4)
Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²
D = | 5 - 12 | / √10
D = 7/√10
D = 2.2135 units
Hence , the distance is 2.2135 units
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Donna is thinking about buying a house that costs $125,000. If she puts down $25,000 and is able to get a 5 percent mortgage, she wants an estimate of her total monthly housing expenses. The average annual cost for owning a house, beyond the 5% cost of mortgage interest, is 4.09 percent of the value of the house. Not including the opportunity cost of the down payment, amortization on the loan, or any tax benefits from homeownership, what will be her monthly cost the first month?
A. $206.25
B. $279.60
C. $842.71
D. $746.43
Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.
To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.
Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:
0.0409 x $125,000 = $5,112.50
This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.
To calculate the monthly cost, we simply divide this by 12:
$5,112.50 / 12 = $426.04
So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.
Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:
Total monthly housing expenses = Mortgage interest + Additional annual costs / 12
Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month
Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71
Hence, Donna can expect her total monthly housing expenses to be approximately $842.71
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X/5-y = m-1 resolver para y
Okay, let's solve this step-by-step:
X/5-y = m-1
Add y to both sides:
X/5 = m
Multiply both sides by 5:
X = 5m
So in this equation, X = 5m.
To find y, we subtract m-1 from both sides of the original equation:
X/5 = 5m
X/5 - (m-1) = 5m - (m-1)
X/5 - m + 1 = 4m
(X - 5m) / 5 = m - 1
X - 5m = 5(m - 1)
X = 20m - 5
So if we let m = any value, we can calculate y. For example:
If m = 3, then:
X = 20*3 - 5
= 55 - 5 = 50
50/X = 5(m - 1) = 5*2 = 10
y = 10
Does this make sense? Let me know if you have any other questions!
7. Given right triangle ABC below, determine sin(A).
The value of Sin A is 5/13.
Option A is the correct answer.
We have,
Sin A = Perpendicular / Hypotenuse
Sin A = BC / AB
And,
BC = 5
AB = 13
Substituting.
Sin A = 5/13
Thus,
The value of Sin A is 5/13.
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Li Wei and Colleen have the same reading assignment. After one week Li Wei has read 90 pages and Colleen has read 126 pages. If Li Wei can you read 30 pages in an hour and Colleen henry 24 pages an hour, when will they be on the same page 
Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.
What are equivalent expressions?Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.
In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.
The number of pages Li Wei can read in a week = 90
The number of pages Collen can read in a week = 126
Li Wei's reading rate per hour = 30 pages
Collen's reading rate per hour = 24 pages
Let the hours that Li Wei and Colleen can be on the same page= x
Expressions:The total number of pages Li Wei can read = 90 + 30x
The total number of pages Colleen can read = 126 + 24x
For Li Wei and Colleen to be on the same, the two expressions are equated.
90 + 30x = 126 + 24x
6x = 36
x = 6
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Find the area of the following figure. Round to the nearest hundred if necessary.
11 cm
A= type your answer...
The area of the semicircle is 47.5 square centimeters
We have to find the area of the semi circle
The diameter of the semicircle is 11 cm
Radius is half of the diameter
Radius = 5.5 cm
Let us find the area of semicircle by formula 1/2(πr²)
Radius = 1/2×3.14×(5.5)²
= 1/2×3.14×30.25
=47.4925 square centimeters
Hence, the area of the semicircle is 47.5 square centimeters
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What function is the inverse of the exponential function y = 4*?
OA
1
y=z.
OC y = log₂ 4
O B. y=(¹)²
O
D. y = log, z
The function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
The inverse of a function f is denoted by [tex]f^{-1[/tex] and it exists only when f is both one-one and onto function. Note that [tex]f^{-1[/tex] is NOT the reciprocal of f. The composition of the function f and the reciprocal function [tex]f^{-1[/tex] gives the domain value of x.
(f o [tex]f^{-1[/tex] ) (x) = ( [tex]f^{-1[/tex] o f) (x) = x
For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation.
The standard exponential function is given as y = abˣ
Given the function,
y = 4ˣ
Replace y with x
[tex]x = 4^y[/tex]
Make y the subject of the formula,
[tex]lnx = ln4^y\\\\lnx = yln4[/tex]
Divide both sides by ln4
lnx/ln4 = y
Hence the function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
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Find the y intercept for a line with a slope or 2 that goes through (5, 4)
Answer:
y- intercept = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = 2 , then
y = 2x + c ← is the partial equation
to find c substitute (5, 4 ) into the partial equation
4 = 2(5) + c = 10 + c ( subtract 10 from both sides )
- 6 = c
that is the y- intercept c = - 6
The number 1.3 is both a(n) __________ and a(n) __________ number.
The number 1.3 is both a rational and an irrational number.
What is the number 1.3?The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.
The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.
So we can conclude that the number 1.3 is both rational and irrational number.
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Find the area of the composite figure
The area of the composite shape is 125units²
What is area of shape?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A composite shape can be defines as a shape created with two or more basic shapes.
The composite shape can be divided into 2 equal squares and a rectangles.
Area of the square = l²
= 5× 5 = 25
For two squares it will be;
25 × 2
= 50 units²
area of the rectangle = l× w
where w is the width
A = 15 × 5
= 75 units²
Therefore the area of the composite shape = 50 + 75 = 125 units²
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18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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Find the distance between (2, 5) and (-5, 8).
58
√58
2√43
2
Answer:
d = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 5 ) and (x₂, y₂ ) = (- 5, 8 )
d = [tex]\sqrt{(-5-2)^2+(8-5)^2}[/tex]
= [tex]\sqrt{(-7)^2+3^2}[/tex]
= [tex]\sqrt{49+9}[/tex]
= [tex]\sqrt{58}[/tex]
Raphael and his four friends are having lunch. They agree to split the bill evenly at the end after adding a 20% tip. If the total bill is $85.60, how much will each person end up paying? A. $25.68 B. $20.54 C. $18.68 D. $17.12
The total amount to each person end up paying $20.54.
To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.
To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.
The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.
Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.
To split this evenly among the five people, we divide by 5:
$102.72 ÷ 5 = $20.54
So each person will end up paying $20.54.
20% of $85.60 is ($85.60 * 0.20) = $17.12
Add the tip to the total bill:
$85.60 + $17.12 = $102.72
Divide the total amount by the number of people (5): $102.72 / 5 = $20.54
Therefore, the answer is B. $20.54.
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Scores on a final exam in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What percent of the students scored above an 83?
Using z - score, the percentage of students above 83 is 15.9%
What is the percentage of students that scored above 83?To find the number of students that scored above 83 can be calculated using z - score formula.
This is given as
z = x - μ / σ
μ = meanσ = standard deviationx = scoreSubstituting the values into the formula;
z = 83 - 75 / 8
z = 1
The z-score is 1
Let's find the percentage of z -score under the score
p(x > 83) = 1 - P(x < 83) = 0.15866
p = 15.9%
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You roll a 6-sided number cube and toss a coin. Let event A = Toss a heads.
What outcomes are in event A?
What outcomes are in event AC?
1. Event A includes the outcomes of H and T,
2. while event AC includes all the possible outcomes of rolling a number cube, which are 1, 2, 3, 4, 5, and 6.
1. Event A is defined as tossing a heads on a coin, regardless of the outcome of rolling a number cube. Therefore, the outcomes in event A are H (heads) and T (tails), since either of these outcomes could occur when rolling a number cube and tossing a coin.
2. Event AC is the complement of event A, i.e., it is the set of outcomes that are not in event A. Since event A contains H and T, the outcomes in event AC are the remaining outcomes that are not in event A, which are all the possible outcomes when rolling a number cube: 1, 2, 3, 4, 5, and 6.
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An art class has 63 minutes of painting for every 54 minutes of instruction. What is the basic ratio of minutes of painting to minutes of instruction
The basic ratio of minutes of painting to minutes of instruction is 7 : 6
What is the basic ratio of minutes of painting to minutes of instructionFrom the question, we have the following parameters that can be used in our computation:
Painting = 63 minutes
Instruction = 54 minutes
The ratio can be represented as
Ratio = Painting : Instruction
When the given values are substituted in the above equation, we have the following equation
Painting : Instruction = 63 : 54
Simplify
Painting : Instruction = 21 : 18
Simplify
Painting : Instruction = 7 : 6
This ratio cannot be simplified
Hence, the solution is 7 : 6
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When Mrs Munyai wanted to swim in her new pool, the temperature of the wate 19 °C and she said she would only swim if the temperature of the water was 25 °C temperature must increase by 6 °C. Calculate what the temperature change would be in °F. You may use the following formula: (°F-32) ÷ 1,8 = °C +
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
The formula to convert the temperature from Celcius to Fahrenheit is:
[tex]\textdegree F = (\textdegree C * 1.8) + 32[/tex]
We need to calculate the temperature change of [tex]6 \textdegree C[/tex] in Fahrenheit:
[tex]\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8[/tex]
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
We can calculate the Fahrenheit temperature of the water and the desired temperature in Fahrenheit:
[tex]^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2[/tex]
[tex]^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77[/tex]
The current temperature of the pool is [tex]66.2 ^{\circ} F[/tex] and the desired temperature is [tex]77 ^{\circ} F[/tex].
Therefore the temperature needs to be increased by:
[tex]\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F[/tex]
which is the same temperature change we calculated earlier in Fahrenheit.
Therefore, the temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
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johnny can build in 3 1/2 lego planes in 60 minutes. how many can he build in 40 minutes?
The number of lego planes that can be build in 40 minutes is A = 2.33
Given data ,
Johnny can build in 3 1/2 lego planes in 60 minutes
On dividing the number of planes he can build in 60 minutes (3 1/2) by 60:
From the proportion , we get
To find out how many planes he can build in 40 minutes, we can multiply the amount he can build in one minute by 40:
3.5 / 60 = A / 40
Multiply by 40 on both sides , we get
A = 2.33
Hence , Johnny can build approximately 2.33 lego planes in 40 minutes
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Mrs. Garcia invests a total of $6331 in two savings accounts. One account yields 8.5% simple interest and the other 8% simple interest. Find the amount placed in each account if she receives a total of $517.68 in interest after one year.
Mrs. Garcia invested $2240 in the 8.5% account and $4091 in the 8% account.
Let x be the amount invested in the 8.5% account, and y be the amount invested in the 8% account. Since the total investment is $6331, we have x + y = 6331.
The total interest received is $517.68, which can be expressed as 0.085x + 0.08y = 517.68, where 0.085 and 0.08 are the decimal equivalents of the interest rates.
We can now solve this system of equations to find x and y. One possible method is to use substitution, where we solve for one variable in terms of the other from one of the equations, and substitute it into the other equation. From x + y = 6331, we have y = 6331 - x. Substituting this into the second equation, we get:
0.085x + 0.08(6331 - x) = 517.68
Simplifying and solving for x, we get:
0.005x + 506.48 = 517.68
0.005x = 11.2
x = 2240
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someone please answer this its confusing me
MA.7.AR.4.1
Johnny and Eleanor went to their local gas station to collect information about the cost of
fuel for compact cars. They observed both regular and premium gas purchases that day and
recorded their data in the table below.
Gallons Purchased 11.5 7.2
10
14.3 6.8
9.7
Cost
$25.23 $15.80 $21.94 $40.63 $14.92 $27.56
Part A. Is there a proportional relationship between the number of gallons of gas sold and
the cost? Explain your answer.
Part B. If the relationship is not proportional, which data value or values should be
changed to make the relationship proportional? What could explain this
difference?
a) The fourth and sixth data points have significantly different ratios.
a) Let's calculate the ratios:
For the first data point:
= 11.5 gallons / $25.23 = 0.4555 gallons per dollar
For the second data point:
= 7.2 gallons / $15.80 = 0.4557 gallons per dollar
For the third data point:
= 10 gallons / $21.94 = 0.4556 gallons per dollar
For the fourth data point:
= 14.3 gallons / $40.63 = 0.3519 gallons per dollar
For the fifth data point:
= 6.8 gallons / $14.92 = 0.4555 gallons per dollar
For the sixth data point:
= 9.7 gallons / $27.56 = 0.3517 gallons per dollar
However, the fourth and sixth data points have significantly different ratios.
b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.
The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.
To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.
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Help me please I need help asap
1. Area of the smaller circle is 100πcm²
2. Area of the bigger circle 800πcm²
How to determine the valueThe formula for the circumference of a circle is expressed as;
Circumference = 2πr
Substitute the values, we get;
20π = 2πr
Divide by the coefficient of r, we get;
r = 10cm
Now, area of a circle is expressed as;
Area = πr²
Substitute the value of the radius
Area = π × 10²
Find the square
Area = 100πcm²
Area of the big circle = 8(area of the small circle)
substitute the values
Area of the big circle = 8(100π)
expand the bracket
Area of the big circle = 800 πcm²
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A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?
The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ
The student can use the following information to establish the AA criterion:
Angle MLN congruent angle QLR (already given)Angle LMN congruent angle LQR or angle LMN congruent angle LRQ (either one will work)These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).
Therefore, the AA congruent for similarity can be congruent .
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Out of 200 students in a senior class, 10 students are varsity athletes and on the honor roll. There are 70 seniors who are varsity athletes and 68 seniors who are on the honor roll. What is the probability that a randomly selected senior is a varsity athlete or on the honor roll? Write your answer as a fraction in simplest form or as a decimal.
Answer: We can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events.
In this case, we want to find the probability that a randomly selected senior is a varsity athlete or on the honor roll. We can define the events as follows:
A = the event that a senior is a varsity athlete
B = the event that a senior is on the honor roll
From the problem statement, we know:
P(A and B) = 10/200 = 1/20
P(A) = 70/200 = 7/20
P(B) = 68/200 = 17/50
Plugging these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 7/20 + 17/50 - 1/20
= 21/50
Therefore, the probability that a randomly selected senior is a varsity athlete or on the honor roll is 21/50.
i dont know the answer to this
The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
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Answer:
Step-by-step explanation:
$6.80 x 19 pounds = $129.2
$4.70 x 18 pounds = $84.6
+___________________
37 pounds = $213.8
$213.8 divided by 37 pounds = 5.77837......
= $5.78 per pound
What do they mean and why please
This exercise uses the normal probability density function and requires the use of either technology or a table of values of the standard normal distribution. The cash operating expenses of the regional phone companies during the first half of 1994 were distributed about a mean of $29.96 per access line per month, with a standard deviation of $2.25. Company A's operating expenses were $28.00 per access line per month. Assuming a normal distribution of operating expenses, estimate the percentage of regional phone companies whose operating expenses were closer to the mean than the operating expenses of Company A were to the mean. (Round your answer to two decimal places.)
The probability of the values of X that are less than 21 is 0.97725.
We have,
The term "standard deviation" refers to a measurement of the data's dispersion from the mean.
A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
u = 20
and SD = 2.25
To find P(X < 21)
So, P(X < 21 )
= 1 - P(X > 21)
Now, P(X > 21)
= P(Z > [(21–20)/2.25]
= P( Z > 1/2.25)
= P(Z > 0.444)
= 0.02275
So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725
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complete question:
Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.