Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.
What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:
θ = 1.75 rad (180° / π rad)
θ = 100.2676
cos 100.2676 = -0.1782 which is now correct since it is nearer to zero
If you toss six fair coins, in how many ways can you obtain at least two heads?
Zooey predicts the movie will be 90 minutes long. If the movie actually is 102 minutes long, what is Zooey's percent error? Round your answer to the nearest tenth of a percent.
An arithmetic sequence is represented in the following table. Enter the missing term of sequence
Answer:
The required 18th term of the given sequence will be -160
Step-by-step explanation:
The A.P. is given to be : 44, 28, 12, -4, ....
First term, a = 44
Common Difference, d = 28 - 44
= -12
We need to find the 18th term of the sequence.
[tex]a_n=a+(n-1)\times d\\\\\implies a_{18}=44+(18-1)\times -12\\\\\implies a_{18}=44+ 17 \times -12\\\\\implies a_{18}=44-201\\\\\implies a_{18}=-160[/tex]
Hence, The required 18th term of the given sequence will be -160
If marc ABC = 184°, what is m∠ABC?
the angle is 1/2 of the arc
184/2 = 92 degrees
It would be half of the intercepted arc which is
360-184 = 176
176/2 = 88 degrees
factoring
x^2-4x-21=0
The sales at a particular bookstore grew from $2090 million in 2000 to $3849 million in 2005. Find an exponential function to model the sales as a function of years since 2000. Give your answer using the form B=Boat
Your science quiz had 17 questions and you answered 13 of the questions correctly. What is your present score?
dived 13 by 17
13/17 = 0.7647
= 76.47%
if you need to round the number it would be 76%, which is a 76 grade
A pile of dirt is cone shaped and it has a height of 10 feet and a diameter of 24 feet. Find the volume. * The answer is NOT 1570.96 or 1570.2*
Please, show me how to solve this. Find the limit as x approaches −8 for the function f(x)=5x+12.
If f(x) is a nth degree polynomial then F^(n+1)(x)=0. True or false and why
Final Answer:
The given statement “If f(x) is a nth degree polynomial then [tex]F^{(n+1)(x)=0[/tex]. True or false and why” is false because the (n+1)st derivative being zero is contingent on the specific value of the leading coefficient in the polynomial. It is not a general rule for all nth degree polynomials.
Explanation:
The statement [tex]\(F^{{(n+1)}(x) = 0\)[/tex] is not universally true for all nth degree polynomials (f(x)). To understand why, consider a general nth degree polynomial [tex]\(f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0\)[/tex], where [tex]\(a_n\)[/tex] is the leading coefficient and [tex]\(a_n \neq 0\)[/tex].
The nth derivative of (f(x)) can be expressed as [tex]\(f^{(n)}(x) = n! \cdot a_n\).[/tex]Now, the (n+1)st derivative, [tex]\(f^{(n+1)}(x)\)[/tex], will be zero if and only if the leading coefficient [tex]\(a_n = 0\)[/tex]. However, this condition is not satisfied in general, as [tex]\(a_n\)[/tex] is assumed to be nonzero for a nontrivial polynomial. Therefore, the (n+1)st derivative is not guaranteed to be zero for all nth degree polynomials.
In mathematical terms,[tex]\(F^{(n+1)}(x)\)[/tex] equals zero if and only if the leading coefficient of (f(x)) is zero, but this is not a universal characteristic of nth degree polynomials. Consequently, the statement is false, and the (n+1)st derivative may not be zero for all x in the domain of the polynomial.
A large tank is filled to capacity with 600 gallons of pure water. brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. the well-mixed solution is pumped out at the same rate. find the number a(t) of pounds of salt in the tank at time t.
To find the amount of salt in the tank at a given time, one can use the equation a(t) = Q - Qe^(-rt). In this case, Q (the quantity of salt at a steady state) equals the pump rate multiplied by the salt concentration (24lb/min), and r (the rate of inflow and outflow of the solution) is the rate at which water is pumped out divided by the volume of the tank (1/100 per min). Substituting these values into the equation gives the salt content at any given time.
Explanation:The quantity of salt in the tank at any given time can be determined by the equation of the form a(t) = Q - Qe^(-rt), in which Q is the quantity of salt that would be in the tank at a steady state (i.e., if enough time had passed that the quantity of salt in the tank stopped changing), r is the rate of inflow and outflow of the solution, and t is the time at which you're trying to determine the number of pounds of salt in the tank.
In this case, Q = rate of inflow x concentration of the inflow, which is 6 gal/min x 4 lb/gal = 24 lb/min. This amount is reached after a sufficient amount of time has passed and the tank has reached a steady state.
The rate, r, is the rate at which the water is pumped out of the tank. In this situation, that's 6 gallons per minute. Since there are 600 gallons of water in the tank at the start, r = 6 gal/min ÷ 600 gallons = 1/100 min^-1.
Therefore, the number of pounds of salt in the tank at any time t is a(t) = Q - Qe^(-rt) = 24 lb/min - 24 lb/min * e^[-(1/100 min^-1)*t].
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Is this statemate true or false?
All parallelograms are special kinds of squares.
Will someone please answer this??
1. Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x= 12.
y = -10 when x = 2
2. Graph the direct variation equation:
y=2x
The marching band is selling cases of fruit for $13 per case. (a) Write an algebraic expression for the cost of f cases of fruit. (b) Evaluate the expression for 250 cases.
An algebraic expression for the cost of f cases of fruit will be (a) z = 13f and the cost for 250 cases will be (b) $3250.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say the cost of the fruit is z
Given,
The marching band is selling cases of fruit for $13 per case.
So for f cases of fruit
z = 13f
And cost of 250 cases = z = 13(150) = $3250
Hence, the algebraic expression for the cost of f cases of fruit will be z = 13f and the cost for 250 cases will be $3250.
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added. Write an equation relating W to T . Then use this equation to find the total amount of water after 19 minutes.
An equation relating W to T is,
W = 700 + 35T
And, Total amount of water after 19 minutes is, 1365 liters
We have to given that,
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute.
There are 700 liters in the pond to start.
Now, Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added.
Hence, an equation relating W to T is,
W = 700 + 35T
So, For T = 19 minutes,
W = 700 + 35 x 19
W = 700 + 665
W = 1365
Therefore, Total amount of water after 19 minutes is, 1365 liters
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Which number is a prime number? 21,22,23,24
A jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 7 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.
Answer:
3x+27+3.5x=397.5
6.5x=370.5
x=57 mph for jeep and travels 199.5 miles in 3.5 hours
x+9=66 mph for B and travels 198 miles in 3 hours
Step-by-step explanation:
speed of jeep=x, time is >>>>> t+0.5 in hours or 3.5 hours here
speed of B=x+9, time is >>>>>>>>>>>> 3 hours
distance is >>>>>>>>> speed time
Hope it Helps.
Answer on: june 11, 2021
Triangle XYZ is reflected across the line x = 3. What is the reflection image of X?
Answer:
It's (7,5)
Step-by-step explanation:
Making use of the fact hat eq. (6.20) is an exact differential expression, show that what is the result of application of this equation to an ideal gas
Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.6321.6 million people. This was an increase of 22% from the population in 1990. What was the population of the country in 1990?
Suppose that 19 inches of wire costs 95 cents. At the same rate, how much (in cents) will 37 inches of wire cost?
0.95/19 = 0.05 cents per inch
37*0.05 = 1.85
it will cost $1.85
Which of the following expressions represents a function?
x2 + y2 = 9
{(4, 2), (4, –2), (9, 3), (9, –3)}
x = 4
2x + y = 5
D is the correct answer the other person who answered explains why.
A chemist has three different acid solutions. The first acid solution contains
25%
acid, the second contains
40%
and the third contains
60%
. He wants to use all three solutions to obtain a mixture of
60
liters containing
45%
acid, using
3
times as much of the
60%
solution as the
40%
solution. How many liters of each solution should be used?
A potter use 4/5 of a pound of clay to make a bowl.How many bowls can the potter make from 12 pounds.
12/1 / 4/5=
12/1 * 5/4 =
60/4 = 15
they can make 15 bowls
which is larger 2/3" x 3-7/16" or 0.6"L x 3.43"W?
William invested $6000 in an account that earns 5.5% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t.
How much did William have in the account after 6 years? (APEX)
Answer:
William have $8273.057 in the account after 6 years.
Step-by-step explanation:
The given formula is [tex]A(t)=P(1+i)^t[/tex]
We have,
P = $6000
r = 5.5% = 0.055
t = 6
A =?
Substituting these values in the above formula to find A
[tex]A(t)=6000(1+0.055)^6\\\\A(t)=8273.057[/tex]
Therefore, William have $8273.057 in the account after 6 years.
find the binomial coefficient: 2012/2011
The binomial coefficient '2012 choose 2011' is calculated using the formula C(n,k) = n! / [(n-k)! * k!]. After substituting the respective values into the formula, we find that the binomial coefficient of '2012 choose 2011' is 2012.
Explanation:The binomial coefficient, often referred to in Mathematics, is generally expressed as 'n choose k' and calculated using the formula: C(n,k) = n! / [(n-k)! * k!]. In this formula, the '!' denotes factorial which means the product of an integer and all the integers below it.
However, the student's question seems to be asking for the binomial coefficient of '2012 choose 2011', which is misinterpreted as a fraction instead.
To calculate it correctly, we would apply the formula mentioned before: C(2012,2011) = 2012! / [(2012-2011)! * 2011!]. Because 2012-2011 equals 1, this simplifies our calculation. The factorial of 1 is 1 itself. Thus, C(2012,2011) = 2012!/ (1! * 2011!), which simplifies to be 2012. So the binomial coefficient of '2012 choose 2011' is 2012.
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Events A and B are mutually exclusive with P(C) = 0.3 and P(B) = 0.2. Then P(Bc) =
The probability of the complement of event B, denoted as Bc, is 0.8.
Explanation:To find the probability of the complement of an event B, denoted as Bc, we can use the formula: P(Bc) = 1 - P(B). Given that events A and B are mutually exclusive, P(B) = 0.2. Therefore, P(Bc) = 1 - 0.2 = 0.8.
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A carpenter is framing a window with wood trim where the length of the window is 9 1/3 feet. If the width of the window is 6 3/4 feet, how many feet of the wood is needed to frame the window?