Answer:
[tex]f'''(x)=\frac{3}{x^{2}}[/tex]
Step-by-step explanation:
We are given with Second-order derivative of function f(x).
[tex]f''(x)=9-\frac{3}{x}[/tex]
We need to find Third-order derivative of the function f(x).
[tex]f''(x)=9-\frac{3}{x}=9-3x^{-1}[/tex]
We know that,
f'''(x) = (f''(x))'
So,
[tex]f'''(x)=\frac{\mathrm{d}\,f''(x)}{\mathrm{d} x}[/tex]
[tex]f'''(x)=\frac{\mathrm{d}\,(9-3x^{-1})}{\mathrm{d} x}[/tex]
[tex]f'''(x)=\frac{\mathrm{d}\,9}{\mathrm{d} x}-\frac{\mathrm{d}\,3x^{-1}}{\mathrm{d} x}[/tex]
[tex]f'''(x)=0-3\frac{\mathrm{d}\,x^{-1}}{\mathrm{d} x}[/tex]
[tex]f'''(x)=-3(-1)x^{-1-1}[/tex]
[tex]f'''(x)=3x^{-2}[/tex]
[tex]f'''(x)=\frac{3}{x^{2}}[/tex]
Therefore, [tex]f'''(x)=\frac{3}{x^{2}}[/tex]
Kellie is given the following information:
If two lines are perpendicular, then they intersect at a right angle. Lines A and B are perpendicular.
She concludes that lines A and B intersect at a right angle. Which statements are true? Check all that apply.
She used inductive reasoning.
She used the law of detachment.
Her conclusion is valid.
The statements can be represented as "if p, then q and if q, then r."
Her conclusion is true.
Answer:
She used inductive reasoning. (False)
She used the law of detachment. (True)
Her conclusion is valid. (True)
The statements can be represented as "if p, then q and if q, then r." (False)
Her conclusion is true. (True)
Step-by-step explanation:
p = Two lines are perpendicular
q = They intersect at Right angles.
Given: A and B are perpendicular
Conclusion: A and B intersect at right angle.
According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.
Statement 1: If p, then q.
Statement 2: p
Conclusion: q
In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.
Answer:
it's b, c, e
Step-by-step explanation:
Place the indicated product in the proper location on the grid. -4x3y2(7xy4)
Answer:
The product is:
[tex]-28x^4y^6[/tex]
Step-by-step explanation:
We need to find product of the terms:
-4x3y2(7xy4)
For multiplication we multiply constants with constants and power of same variables are added
[tex]-4x^3y^2(7xy^4)\\=(-4*7)(x^3*x)(y^2*y^4)\\=(-28)(x^{3+1})(y^{2+4})\\=(-28)(x^4)(y^6)\\=-28x^4y^6[/tex]
So, the product is:
[tex]-28x^4y^6[/tex]
Suppose that the number of calls coming per minute into an airline reservation center follows a Poisson distribution. Assume that the mean is 3 calls per minute. The probability that at least two calls are received in a given two-minute period is _______.
Answer: 0.9826
Step-by-step explanation:
Given : Mean : [tex]\lambda =3\text{ calls per minute}[/tex]
For two minutes period the new mean would be :
[tex]\lambda_1=2\times3=6\text{ calls per two minutes}[/tex]
The formula to calculate the Poisson distribution is given by :_
[tex]P(X=x)=\dfrac{e^{-\lambda_1}\lambda_1^x}{x!}[/tex]
Then ,the required probability is given by :-
[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\=1-(\dfrac{e^{-6}6^0}{0!}+\dfrac{e^{-6}6^1}{1!})\\\\=1-0.0173512652367\\\\=0.982648734763\approx0.9826[/tex]
Hence, the probability that at least two calls are received in a given two-minute period is 0.9826.
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to: = > (a) -a x + 4x12 4x1x38x231; (b) 3-33 + 4xrj224x3122a3= 1; (c) 4a7 2x1 2x1X36x2a3 = 1. 2. Solve the following systems of differential equations using the matrix exponential technique 3x 4 (a) x(0) = 5, y(0) = 1; 4x-3y 3.x y(0) = 9, y(0) = 3; -2x 6x2y
Answer:
678
Step-by-step explanation:
A family has five children. The probability of having a girl is 2 What is the probability of having no girls? Round the answer to the fourth decimal place
Answer: Hence, the probability of having no girls is 0.0313.
Step-by-step explanation:
Since we have given that
Number of children a family has = 5
Number of outcomes would be [tex]2^5=32[/tex]
Probability of having a girl = [tex]\dfrac{1}{2}=0.5[/tex]
We need to find the probability of having no girls.
P(no girls ) = P( all boys )
So, it becomes,
[tex]P(all\ boys)=(0.5)^5=0.03125\approx 0.0313[/tex]
Hence, the probability of having no girls is 0.0313.
The average annual salary for 35 of a company’s 1200 accountants is $57,000. This describes a parameter.
yeah it does because $68,000 is a numerical description of a sample of annual salaries. so it is only a PARAMETER
--mark brainliest please! thank you and i hope this helps
Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = -6/7 . Find the exact values of the five remaining trigonometric functions of θ. Find the exact values of the five remaining trigonometric functions of θ.
let's recall that on the IV Quadrant the sine/y is negative and the cosine/x is positive, whilst the hypotenuse is never negative since it's just a distance unit.
[tex]\bf \stackrel{\textit{on the IV Quadrant}}{cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}}\qquad \impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf tan(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}}\qquad \qquad sec(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}}[/tex]
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies -\cfrac{7\sqrt{85}}{85}} \\\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies \cfrac{6\sqrt{85}}{85}}[/tex]
Answer:
These are the five remaining trigonometric functions:
tanθ = - 7/6secθ = (√85) / 6cosθ = 6(√85) / 85sinθ = - 7(√85) / 85cscθ = - (√85)/7Explanation:
Quadrant IV corresponds to angle interval 270° < θ < 360.
In this quadrant the signs of the six trigonometric functions are:
sine and cosecant: negativecosine and secant: positivetangent and cotangent: negativeThe expected values of the five remaining trigonometric functions of θ are:
1) Tangent:
tan θ = 1 / cot (θ) = 1 / [ -6/7] = - 7/62) Secant
sec²θ = 1 + tan²θ = 1 + (-7/6)² = 1 + 49/36 = 85/36sec θ = ± (√85)/ 6
Choose positive, because secant is positive in Quadrant IV.
sec θ = (√85) / 6
3) Cosine
cosθ = 1 / secθ = 6 / (√85) = 6 (√85) / 854) Sine
sin²θ + cos²θ = 1 ⇒ sin²θ = 1 - cos²θ = 1 - [6(√85) / 85] ² =sin²θ = 1 - 36×85/(85)² = 1- 36/85 = 49/85
sinθ = ± 7 / (√85) = ± 7(√85)/85
Choose negative sign, because it is Quadrant IV.
sinθ = - 7 (√85) / 85
5) Cosecant
cscθ = 1 / sinθ = - 85 / (7√85) = - (√85) / 7Raise the quality in parentheses to the indicated exponent, and slim lift the resulting expression with positive exponents.
For this case we have the following expression:
[tex](\frac {-27x ^ 0 * y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition we have to:
[tex]a^0= 1[/tex]
So:
[tex](\frac {-27y ^ {- 2}} {54x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
Simplifying:
[tex](\frac {-y ^ {- 2}} {2x ^ {- 5} * y ^ {- 4}}) ^ {- 2} =[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, rewriting the expression we have:
[tex]\frac {-y ^ {- 2 * -2}} {4x ^ {- 5 * -2} * y ^ {- 4 * -2}} =\\\frac {-y ^ {4}} {4x ^ {10} * y ^ {8}} =[/tex]
SImplifying:
[tex]\frac {-y ^ {4-8}} {4x ^ {10}} =\\\frac {-y ^ {- 4}} {4x ^ {10}} =\\- \frac {1} {4x ^ {10} y^ {4}}[/tex]
Answer:
[tex]- \frac {1} {4x ^ {10} y ^ {4}}[/tex]
Someone can you please help me on number 74
Answer:
9t^3 +t^2
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of the sides. The side lengths are represented by the polynomials shown, so the perimeter (P) is their sum:
P = (4t^3 -5) + (4t^3 -5) + (t^2 +9) + (t^3 -t^2 -11) + (t^2 +12)
Rearranging to group like terms:
P = (4t^3 +4t^3 +t^3) + (t^2 -t^2 +t^2) + (-5 -5 +9 -11 +12)
P = 9t^3 +t^2
The perimeter of the figure is represented by the polynomial 9t^3 +t^2.
Answer:
[tex]9t^3+t^2[/tex]
Step-by-step explanation:
We are given a figure of a polygon with mentioned side lengths and we are to find the perimeter of it.
For that, we will simply add the given side lengths and simplify them.
Perimeter of polygon = [tex] ( 4 t ^ 3 - 5 ) + ( 4 t ^ 3 - 5 ) + ( t ^ 2 + 9 ) + ( t ^ 2 + 1 2 ) + ( t ^ 3 - t ^ 2 - 1 1 ) [/tex]
= [tex] 4 t ^ 3 + 4 t ^ 3 + t ^ 3 + t ^ 2 - t ^ 2 + t ^ 2 - 5 - 5 + 9 - 1 1 + 1 2 [/tex]
Perimeter of polygon = [tex]9t^3+t^2[/tex]
Write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (–4, 0).
Answer:
[tex]y^{2}=-16x[/tex]
Step-by-step explanation:
we know that
The standard equation of a horizontal parabola is equal to
[tex](y-k)^{2}=4p(x-h)[/tex]
where
(h,k) is the vertex
(h+p,k) is the focus
In this problem we have
(h,k)=(0,0) ----> vertex at origin
(h+p,k)=(-4,0)
so
h+p=-4
p=-4
substitute the values
[tex](y-0)^{2}=4(-4)(x-0)[/tex]
[tex]y^{2}=-16x[/tex]
In the 1980s an average mortgage rate was around 18.5 how much less per month would a 150000 30 year mortgage by today if the current rate were 5 %
Answer:
$1516.69 per month less
Step-by-step explanation:
The formula for the monthly payment A on a loan of principal P, annual rate r, for t years is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
For the 18.5% loan, the monthly payment is ...
A = 150000(.185/12)/(1 -(1 +.185/12)^(-12·30)) ≈ 2321.92
For the 5% loan, the monthly payment is ...
A = 150000(.05/12)/(1 -(1 +.05/12)^-360) ≈ 805.23
The mortgage at 5% would be $1516.69 less per month.
Final answer:
To determine how much less per month a $150,000 30-year mortgage would be at a 5% interest rate compared to an 18.5% rate, calculate monthly payments for both scenarios and subtract the lower payment from the higher one.
Explanation:
The question asks to compare monthly mortgage payments in two different interest rate scenarios for a 30-year, $150,000 mortgage: first at an 18.5% interest rate which was the average in the 1980s, and second at the current rate of 5%. To find out how much less the monthly payment would be at 5% compared to 18.5%, we can use the formula for calculating monthly mortgage payments:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
where:
M is your monthly payment.
P is the principal loan amount, $150,000 in this case.
i is your monthly interest rate. The annual rate needs to be divided by 12.
n is the number of payments (the number of months you will be paying the loan).
Calculating the monthly payment for an 18.5% interest rate over 30 years:
P = $150,000
i = 18.5% annual interest rate / 12 months = 1.5417% monthly interest rate
n = 30 years * 12 months/year = 360 payments
Doing the same calculation at a 5% interest rate:
P = $150,000
i = 5% annual interest rate / 12 months = 0.4167% monthly interest rate
n = 30 years * 12 months/year = 360 payments
After computing the monthly payments for both interest rates, we then subtract the monthly payment at 5% from the monthly payment at 18.5% to determine how much less it would be. As this is a high school-level mathematics problem, we use algebraic operations and functions to answer the question.
Help need help on this 3 math problems !!!
8. Determine whether the function shown is constant, linear, quadratic, or none of these. m(x)=13/6
A. Linear
B. Quadratic
C. None of these
D. Constant
6. Does the following equation determine y to be a function of x?
y2 = x + 3
A. No
B. Yes
C. Only when x = 1
D. Sometimes
16. Solve the system. y=1/7x-4 x=7y+1
A. No solution
B. (7, –3)
C. (–13, –2)
D. There are an infinite number of solutions
Answer:
8. D. Constant
6. A. No
16. A. No solution
Step-by-step explanation:
8. There is no "x" on the right side of the equal sign in the function definition. There is only the constant 13/6. The function shown is constant.
__
6. The equation will graph as a parabola that opens to the right. Solving for y, you get ...
y = ±√(x+3)
This is double-valued. A relation that gives two values for the same value of x is not a function.
__
16. In standard form, the two equations are ...
x -7y = 28x -7y = 1These equations are "inconsistent". There are no values of x and y that can make them both be true. Thus, there is no solution.
Manuel and Ruben both have bank accounts. The system of equations models their balances after x weeks. y = 11.5x + 22 y = –13x + 218 Their balances will be the same after weeks. Their balances will be $
Answer:
The equal balances will be $114 after 8 weeks
Step-by-step explanation:
* Lets study the information in the problem
- Manuel and Ruben both have bank accounts
- The system of equations models their balances y after x weeks
- Manuel balance is y = 11.5x + 22
- Ruben balance is y = -13x + 218
- After x weeks they will have same balances, means the values of y
will be equal at the same values of x
- The solve the problem we will equate the two equations to find x
and then substitute this x in on of the equation s to find the
balance y
- Lets do that
∵ Manuel balance is y = 11.5x + 22
∵ Ruben balance is y = -13x + 218
∵ After x weeks their balances will be equal
- Equate the equations
∴ 11.5x + 22 = -13x + 218
- add 13 x for both sides
∴ 11.5x + 13x + 22 = 218
∴ 24.5x + 22 = 218
- subtract 22 from both sides
∴ 24.5x = 218 - 22
∴ 24.5x = 196
- Divide both sides by 24.5
∴ x = 8
- Their balances will be equals after 8 weeks
- To find the balance substitute x by 8 in any equation
∵ y = 11.5x + 22
∵ x = 8
∴ y = 11.5(8) + 22
∴ y = 92 + 22 = 114
∴ The equal balances will be $114
* The equal balances will be $114 after 8 weeks
Answer:
The equal balances will be $114 after 8 weeks
Step-by-step explanation:
. Need help !!! on 2 math questions
The height in feet of a ball dropped from a 150 ft. Building is given by h(t) = –16t2 + 150, where t is the time in seconds after the ball is dropped. Find h(2) and interpret its meaning. Round your answer to the nearest hundredth.
A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.
B. h(2) = 3.04 means that after 2 seconds, the height of the ball has dropped by 3.04 ft.
C. h(2) = 3.04 means that after 2 seconds, the height of the ball is 3.04 ft.
D. h(2) = 86.00 means that after 2 seconds, the height of the ball has dropped by 86.00 ft.
15. The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides.
A. 16 cm; 21 cm; 32 cm
B. 15 cm; 21 cm; 33 cm
C. 15 cm; 22 cm; 32 cm
D. 17 cm; 21 cm; 31 cm
Answer:
Part 1) Option A. h(2) = 86.00 means that after 2 seconds, the height of the ball is 86.00 ft.
Part 2) Option A. 16 cm; 21 cm; 32 cm
Step-by-step explanation:
Part 1)
we have
[tex]h(t)=-16t^{2}+150[/tex]
where
t ----> is the time in seconds after the ball is dropped
h(t) ----> he height in feet of a ball dropped from a 150 ft
Find h(2)
That means ----> Is the height of the ball 2 seconds after the ball is dropped
Substitute the value of t=2 sec in the equation
[tex]h(2)=-16(2)^{2}+150=86\ ft[/tex]
therefore
After 2 seconds, the height of the ball is 86.00 ft.
Part 2) The perimeter of a triangle is 69 cm. The measure of the shortest side is 5 cm less than the middle side. The measure of the longest side is 5 cm less than the sum of the other two sides. Find the lengths of the sides
Let
x----> the measure of the shortest side
y ----> the measure of the middle side
z-----> the measure of the longest side
we know that
The perimeter of the triangle is equal to
P=x+y+z
P=69 cm
so
69=x+y+z -----> equation A
x=y-5 ----> equation B
z=(x+y)-5 ----> equation C
substitute equation B in equation C
z=(y-5+y)-5
z=2y-10 -----> equation D
substitute equation B and equation D in equation A and solve for y
69=(y-5)+y+2y-10
69=4y-15
4y=69+15
4y=84
y=21 cm
Find the value of x
x=21-5=16 cm
Find the value of z
z=2(21)-10=32 cm
The lengths of the sides are 16 cm, 21 cm and 32 cm
If jobs arrive every 15 seconds on average, what is the probability of waiting more than 30 seconds?
Answer: 0.14
Step-by-step explanation:
Given: Mean : [tex]\lambda=15\text{ per seconds}[/tex]
In minutes , Mean : [tex]\lambda=4\text{ per minute}[/tex]
The exponential distribution function with parameter [tex]\lambda[/tex] is given by :-
[tex]f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0[/tex]
The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-
[tex]P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14[/tex]
Hence, the probability of waiting more than 30 seconds = 0.14
The probability of waiting more than 30 seconds for a job, when jobs arrive every 15 seconds on average, can be calculated using the Poisson distribution model. The probability is approximately 13.5%.
Explanation:This problem involves the concept of Poisson distribution, which is a mathematical concept used to model events such as the arrival of customers in a given time interval. Since the question states that jobs arrive every 15 seconds on average, we can use this information to calculate the probability of waiting more than 30 seconds.
In a Poisson distribution, the average rate of arrival (λ) is 1 job every 15 seconds. This rate can be converted to a rate per 30 seconds by multiplying by 2, giving us λ=2. The probability that no jobs arrive in a 30-second interval in a Poisson distribution is given by the formula:
P(X=0) = λ^0 * e^-λ / 0! = e^-2 ≈ 0.135
This means that the probability of waiting more than 30 seconds is approximately 0.135, or 13.5%.
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b. Two events are dependent if the occurrence of one event changes to occurrence of the second event. True or False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
If 2 events are independent, then one event will not affect the other
Find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28. Round your answer to four decimal places, if necessary.
Answer:
The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
Step-by-step explanation:
We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.
The standard normal table represents the area under the curve.
[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex] .....(1)
According to the standard normal table, we get
[tex]P(z<-2.94)=0.0016[/tex]
[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]
Substitute these values in equation (1).
[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]
Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 is 0.9903 square units.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be
The standard normal table represents the area under the curve.
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1
According to the standard normal table, we have
[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]
Substitute these values in equation 1, we have
[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]
More about the normal distribution link is given below.
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Five Card Draw is one of most basic forms of poker, and it's the kind of poker you're used to seeing in movies and on TV. This game has been around for a long time, and has been played in countless home games and card rooms across the nation. Play begins with each player being dealt five cards, one at a time, all face down. The remaining deck is placed aside, often protected by placing a chip or other marker on it. Players pick up the cards and hold them in their hands, being careful to keep them concealed from the other players, then a round of betting occurs. Some combinations of five-card hand have special names such as full house, royal flush, four of a kind, etc. Let`s find some 5-card combinations. Order of the drawn card does not matter. a) A flush is a poker hand, where all five cards are of the same suit, but not in sequence. Compute the number of a 5-card poker hands containing all diamonds.
Answer:
1287
Step-by-step explanation:
The number of combinations of 13 diamonds taken 5 at a time is ...
13C5 = 13·12·11·10·9/(5·4·3·2·1) = 13·11·9 = 1287
Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $450 for the coverage they need. Their insurance company offers a discount of 6 percent if they install dead-bolt locks on all exterior doors. The couple can also receive a discount of 2 percent if they install smoke detectors on each floor. They have contacted a locksmith who will provide and install dead-bolt locks on the two exterior doors for $50 each. At the local hardware store, smoke detectors cost $7 each, and the new house has two floors. Dave and Ellen can install them themselves. a. What discount will Dave and Ellen receive if they install the dead-bolt locks? Annual discount for deadbolts b. What discount will Dave and Ellen receive if they install smoke detectors? Annual discount for smoke detectors
Dave and Ellen could annually save $27 by installing dead-bolts and $9 by installing smoke detectors. This amounts to a significant discount on their homeowner's insurance premium.
Explanation:Dave and Ellen's annual homeowner's insurance premium is $450. If they install dead-bolts on all the exterior doors, they would receive a 6 percent discount, while smoke detector installations would fetch them a 2 percent discount. Let's calculate these discounts:
A. Dead-bolts discount: 6 percent of $450 translates to $(450*(6/100)) which equals $27.
B. Smoke detectors discount: 2 percent of $450would be $(450*(2/100)) that equals $9.
To summarize, the couple could annualy save $27 by installing dead-bolts and $9 by installing smoke detectors, which is a substantial reduction on the insurance premium.
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Dave and Ellen can save $27 annually by installing dead-bolt locks and $9 annually by installing smoke detectors. Total savings from both installations would be $36 annually.
Let's break down the problem step by step to calculate the discounts that Dave and Ellen will receive if they install dead-bolt locks and smoke detectors.
Part (a): Discount for Dead-Bolt Locks
1. Annual premium: $450
2. Discount for dead-bolt locks: 6%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the dead-bolt locks:
Discount amount for dead-bolt locks = 450 × [tex]\frac{6}{100} \][/tex]
Discount amount for dead-bolt locks = 450 × 0.06
Discount amount for dead-bolt locks = 27
Thus, Dave and Ellen will receive an annual discount of $27 if they install dead-bolt locks on all exterior doors.
Part (b): Discount for Smoke Detectors
1. Annual premium: $450
2. Discount for smoke detectors: 2%
The discount amount is calculated as follows:
[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]
So, for the smoke detectors:
Discount amount for smoke detectors} = 450 × [tex]\frac{2}{100}[/tex]
Discount amount for smoke detectors} = 450 × 0.02
Discount amount for smoke detectors} = 9
Thus, Dave and Ellen will receive an annual discount of $9 if they install smoke detectors on each floor of their house.
CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 234 dollars. You take a simple random sample of 61 auto insurance policies. Find the probability that a single randomly selected value is at least 960 dollars.
Answer: 0.42
Step-by-step explanation:
Given: Mean : [tex]\mu=954\text{ dollars}[/tex]
Standard deviation : [tex]234\text{ dollars}[/tex]
Sample size : [tex]n=61[/tex]
The formula to calculate z score is given by :-
[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For X=960
[tex]z=\dfrac{960 -954}{\dfrac{234}{\sqrt{61}}}=0.200262812203\approx0.2[/tex]
The p-value =[tex]P(X\geq960)=1-P(X<960)=1-P(z<0.2)=1-0.5792597=0.4207403\approx0.42[/tex]
Hence, the probability that a single randomly selected value is at least 960 dollars = 0.42
the center of a circle represent by the equation (x+9)^2+(y-6)^2=10^2 is___. options.... (-9,6), (-6,9), (6,-9) ,(9,-6)
Answer:
(-9, 6)
Step-by-step explanation:
It's all about pattern matching.
A circle centered at (h, k) with radius r has the equation ...
(x -h)^2 + (y -k)^2 = r^2
Comparing this pattern to the equation you have, you can see that ...
h = -9k = 6r = 10Then the center is (h, k) = (-9, 6).
Answer:
(-9, 6)
Step-by-step explanation:
i took the test
Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches. The ratio is (Type an integer or a simplified fraction)
Answer: The ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
Step-by-step explanation:
Since we have given that
Radius of first sphere = 5 inches
Radius of second sphere = 10 inches
We need to find the ratio of volume of first sphere to volume of second sphere:
As we know the formula for "Volume of sphere ":
[tex]Volume=\dfrac{4}{3}\pi r^3[/tex]
So, it becomes,
Ratio of first volume to second volume is given by
[tex]\dfrac{4}{3}\pi (5)^3:\dfrac{4}{3}\pi (10)^3\\\\=5^3:10^3\\\\=125:1000\\\\=1:8[/tex]
Hence, the ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]
The ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches is 1/8.
Explanation:To find the ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Let's calculate the volumes of the two spheres:
For the sphere with a radius of 5 inches:
V1 = (4/3)π(5)³ = (4/3)π(125) = 500π inches³
For the sphere with a radius of 10 inches:
V2 = (4/3)π(10)³ = (4/3)π(1000) = 4000π inches³
Therefore, the ratio of the two volumes is:
R = V1/V2 = (500π)/(4000π) = 1/8
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A study claims that the mean age of online dating service users is 40 years. Some researchers think this is not accurate and want to show that the mean age is not 40 years. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. Select the correct answer below: H0: μ≥40; Ha: μ<40 H0: μ≤40; Ha: μ>40 H0: μ≠40; Ha: μ=40 H0: μ=40; Ha: μ≠40
Answer: [tex]H_0:\mu=40[/tex]
[tex]H_0:\neq40[/tex]
Step-by-step explanation:
A null hypothesis is a hypothesis where a researcher generally try to disprove, it says that there is no statistically significant relationship between the two variables . An alternative hypothesis says that there is a statistical significance between two variables.Claim 1. : Mean age of online dating service users is 40 years.
i.e. [tex]\mu=40[/tex], since it has equals sign so we take this as null hypothesis.
Claim 2. : Mean age of online dating service users is not 40 years.
[tex]\mu\neq40[/tex]
⇒ Null Hypothesis : [tex]H_0:\mu=40[/tex]
Alternative hypothesis : [tex]H_0:\neq40[/tex]
what is the length of pr?
help me, thank tou so much :)
Answer:9
Step-by-step explanation:
1st triangle is similar to the second one as the angles of both of the triangles are the same..
So we know the ratio of the similar lines will be constant.it means,
XY/PQ=XZ/PR=YZ/QR
So,Xy/PQ=XZ/PR
21/7=27/x
X=(27×7)/21
X=9
Thats the value of pr..
Which of the following vectors can be written as a linear combination of the vectors (1, 1, 2), (1, 2, 1) and (2, 1, 5)? (0.4,3.7,-1.5) (0.2,0) None of the selections is correct. All the selections are correct
Answer with explanation:
Let, A=[1,1,2]
B=[1,2,1]
C=[2,1,5]
⇒Now, Writing vector , A in terms of Linear combination of C and B
A=x B +y C
⇒[1,1,2]=x× [1,2,1] + y×[2,1,5]
1.→1 = x +2 y
2.→ 1=2 x +y
3.→ 2= x+ 5 y
Equation 3 - Equation 1
→3 y=1
[tex]y=\frac{1}{3}[/tex]
[tex]1=x+\frac{2}{3}\\\\x=1 -\frac{2}{3}\\\\x=\frac{1}{3}[/tex]
So, Vector A , can be written as Linear Combination of B and C.
⇒Now, Writing vector , B in terms of Linear combination of A and C
Now, let, B = p A+q C
→[1,2,1]=p× [1,1,2] +q ×[2,1,5]
4.→1= p +2 q
5.→2=p +q
6.→1=2 p +5 q
Equation 5 - Equation 4
-q =1
q= -1
→2= p -1
→p=2+1
→p=3
So, Vector B , can be written as Linear Combination of A and C.
⇒Now, Writing vector , C in terms of Linear combination of A and B
C=m A + n B
[2,1,5] = m×[1,1,2] + n× [1,2,1]
7.→2= m+n
8.→1=m +2 n
9.→5=2 m + n
Equation 8 - Equation 7
n= -1
→m+ (-1)=2
→m=2+1
→m=3
So, Vector C , can be written as Linear Combination of A and B.
So, All the three vectors , A=[1,1,2],B=[1,2,1],C=[2,1,5] can be written as Linear combination of each other.
⇒≡But , the two vectors, (0.4,3.7,-1.5) (0.2,0),can't be written as Linear combination of each other as first vector is of order, 1×3, and second is of order, 1×2.
None of the selections is correct.
How to apply linear combinations and linear independence to determine the existence of a relationship with a given vector
In this case, we must check the existence of a set of real coefficients such that the following two linear combinations exist:
[tex]\alpha_{1}\cdot (1, 1, 2)+\alpha_{2}\cdot (1, 2,1)+\alpha_{3}\cdot (2, 1, 5) = (0.4, 3.7, -1.5)[/tex] (1)
[tex]\alpha_{4}\cdot (1,1,2)+\alpha_{5}\cdot (1,2,1) + \alpha_{6}\cdot (2,1,5) = (0, 2, 0)[/tex] (2)
Now we proceed to solve each linear combination:
First system[tex]\alpha_{1}+\alpha_{2}+2\cdot \alpha_{3} = 0.4[/tex]
[tex]\alpha_{1}+2\cdot \alpha_{2}+\alpha_{3} = 3.7[/tex]
[tex]2\cdot \alpha_{1}+\alpha_{2}+5\cdot \alpha_{3} = -1.5[/tex]
The system has no solution, since the third equation is a linear combination of the first and second ones.
Second system[tex]\alpha_{4}+\alpha_{5}+2\cdot \alpha_{6} = 0[/tex]
[tex]\alpha_{4}+2\cdot \alpha_{5}+\alpha_{6} = 2[/tex]
[tex]2\cdot \alpha_{4}+\alpha_{5}+5\cdot \alpha_{6} = 0[/tex]
The system has no solution, since the third equation is a linear combination of the first and second ones.
None of the selections is correct. [tex]\blacksquare[/tex]
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3) An open top box is to be constructed out of a 90 inch by 70 inch piece of cardboard by cutting squares out of the corners and then folding the side flaps up. If the squares all have sides of 15 inches, find the following.
a) Volume in cubic inches.
b) Volume in cubic feet.
c) Volume in cubic yards.
Answer:
a) The volume in cubic inches is 36000
b) The volume in cubic feet is 125/6
c) The volume in cubic yard is 125/162
Step-by-step explanation:
* Lets study the information of the problem to solve it
- The dimensions of the piece of cardboard are 90 inches by 70 inches
- The side of the cutting square is 15 inches
- The squares are cutting from each corner
∴ Each dimension of the cardboard will decrease by 2 × 15 inches
∴ The new dimensions of the piece of cardboard are;
90 - (15 × 2) = 90 - 30 = 60 inches
70 - (2 × 15) = 70 - 30 = 40 inches
- The dimensions of the box will be:
# Length = 60 inches
# width = 40 inches
# height = 15 inches
- The volume of any box with three different dimensions is
V = Length × width × height
∵ The length = 60 inches
∵ The width = 40 inches
∵ The height = 15 inches
∴ V = 60 × 40 × 15 = 36000 inches³
a) The volume in cubic inches is 36000
* Now lets revise how to change from inch to feet
- 1 foot = 12 inches
∵ 1 foot = 12 inches
∴ 1 foot³ = (12)³ inches³
∴ 1 foot³ = 1728 inches³
∵ The volume of the box is 36000 inches³
∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6
b) The volume in cubic feet is 125/6
* Now lets revise how to change from feet to yard
- 1 yard = 3 feet
∵ 1 yard = 3 feet
∴ 1 yard³ = (3)³ feet³
∴ 1 yard³ = 27 feet³
∵ The volume of the box is 125/6 feet³
∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162
c) The volume in cubic yard is 125/162
Answer:
3600 cubic inches , 2.08 cubic feet , 0.0771 cubic yards
Step-by-step explanation:
Here we are given that the open box has been constructed from a card board with length 90 inches and width 70 inches by
1. cutting a square card board
2. of each side 15 inches
Hence when we are done with folding it for our cuboid , we find our new
1. Length = 90-15-15 = 60 inches
2. width = 70-15-15 = 40 inches
3. Height = 15 inches
Now we know the volume of any cuboid is given as
V= Length * width * height
= 60*40*15
= 3600 cubic inches
Part 2 . Now let us convert them into cubic feet
1 cubic inch = 0.000578704 cubic feet
Hence 3600 cubic inches = 3600 * 0.000578704 cubic feet
=2.083 cubic feet
Part 3. Now let us convert them into cubic yards
1 cubic inch = 0.0000214335 cubic yards
Hence 3600 cubic inches = 3600 * 0.0000214335 cubic yards
= 0.0771 cubic yards
Chords and arcs. Can someone please help me with this and explain???20 points
Answer:
89
Step-by-step explanation:
So the line segment CD is 12.7 and half that is 6.35. I wanted this 6.35 so I can look at the right triangle there and find the angle there near the center. This will only be half the answer. So I will need to double that to find the measure of arc CD.
Anyways looking at angle near center in the right triangle we have the opposite measurement, 6.35, given and the hypotenuse measurement, 9.06, given. So we will use sine.
sin(u)=6.35/9.06
u=arcsin(6.35/9.06)
u=44.5 degrees
u represented the angle inside that right triangle near the center.
So to get angle COD we have to double that which is 89 degrees.
So the arc measure of CD is 89.
if a*b represents the number of integers greater than a and less than b, what is the value of -2π*3√2
(a) 13 (b) 12 (c) 11 (d) 10
Answer:
11
Step-by-step explanation:
-2×pi is approximately-6.28
3×sqrt(2) is approximately 4.24
Now if you really need... just list out the integers between those two numbers and then count like so: -6,-5,-4,-3,-2,-1,0,1,2 3,4
That is 11 integers
The question is about finding the number of integers between -2π and 3√2. This involves understanding the definition of the function a*b, and then applying this to the given values. The correct answer is 11.
Explanation:The function a*b defined in this problem represents the number of integers greater than a and less than b.
When we substitute a with -2π and b with 3√2, we are basically finding the number of integers between -2π and 3√2.
Knowing that -2π is approximately -6.28, and 3√2 which is approximately 4.24, we count the integers that fall between these two numbers.
Our list of integers will be: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4. Hence, the answer is 11 (option c).
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Determine whether f(x)=-5x^2-10x+6 has a maximum or a minimum value. Find that value and explain how you know.
Answer:
(-1, 11) is a max value; parabola is upside down
Step-by-step explanation:
We can answer this question backwards, just from what we know about parabolas. This is a negative x^2 parabola, so that means it opens upside down. Because of this, that means that there is a max value.
The vertex of a parabola reflects either the max or the min value. In order to find the vertex, we put the equation into vertex form, which has the standard form:
[tex]y=a(x-h)^2+k[/tex]
where h and k are the coordinates of the vertex.
To put a quadratic into vertex form, you need to complete the square. That process is as follows. First, set the quadratic equal to 0. Then make sure that the leading coefficient is a positive 1. Ours is a -5 so we will have to factor it out. Then, move the constant to the other side of the equals sign. Finally, take half the linear term, square it, and add it to both sides. We will get that far, and then pick up with the rest of the process as we come to it.
[tex]-5x^2-10x+6=y[/tex]
Set it to equal zero:
[tex]-5x^2-10x+6=0[/tex]
Now move the 6 to the other side:
[tex]-5x^2-10x=-6[/tex]
Factor out the -5:
[tex]-5(x^2+2x)=-6[/tex]
Take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1, so add it to both sides. Keep it mind that we have the =5 out front of those parenthesis that will not be forgotten. So we are not adding in a +1, we are adding in a (+1)(-5) which is -5:
[tex]-5(x^2+2x+1)=-6-5[/tex]
In completing the square, we have created a perfect square binomial on the left. Stating that binomial along with simplifying on the right gives us:
[tex]-5(x+1)^2=-11[/tex]
Now, bring the -11 over to the other side and set it back to equal y and you're ready to state the vertex:
[tex]-5(x+1)^2+11=y[/tex]
The vertex is at (-1, 11)
How do I calculate this? Is there a formula?
A suspension bridge with weight uniformly distributed along its length has twin towers that extend 95 meters above the road surface and are 1200 meters apart. The cables are parabolic in shape and are suspended from the tops of the towers. The cables touch the road surface at the center of the bridge. Find the height of the cables at a point 300 meters from the center. (Assume that the road is level.)
Answer:
Height of cables = 23.75 meters
Step-by-step explanation:
We are given that the road is suspended from twin towers whose cables are parabolic in shape.
For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.
Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of [tex]x = 600[/tex] or [tex]x = -600[/tex], and y at 95.
We know that the equation of a parabola is in the form [tex]y=ax^2[/tex] and here it passes through the point [tex](600, 95)[/tex].
[tex]y=ax^2[/tex]
[tex]95=a \times 600^2[/tex]
[tex]a=\frac{95}{360000}[/tex]
[tex]a=\frac{19}{72000}[/tex]
So new equation for parabola would be [tex]y=\frac{19x^2}{72000}[/tex].
Now we have to find the height [tex](y)[/tex]of the cable when [tex]x= 300[/tex].
[tex]y=\frac{19 (300)^2}{72000}[/tex]
y = 23.75 meters
Answer: 23.75 meters
Step-by-step explanation:
If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:
[tex]y = a (x-0) ^ 2 + 0\\\\y = ax ^ 2[/tex]
We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.
Thus:
[tex]95 = a (600) ^ 2[/tex]
[tex]a = \frac{95} {600 ^ 2}\\\\a = \frac {19} {72000}[/tex]
Then the equation is:
[tex]y = \frac{19}{72000} x ^ 2[/tex]
Finally the height of the cables at a point 300 meters from the center is:
[tex]y = \frac{19}{72000}(300) ^ 2[/tex]
[tex]y =23.75\ meters[/tex]