Final answer:
To find (g°f)(0), evaluate f(0) to get 6, then apply g to this result to also get 6. Hence, (g°f)(0) equals 6.
Explanation:
The question is asking to evaluate the composition of two functions, (g°f)(x), at the value x = 0. Composition of functions involves applying one function to the result of another. In this case, since f(x) = 2x + 6 and g(x) = x, we first find f(0), which is the result of plugging 0 into f(x).
Let's calculate:
f(0) = 2(0) + 6 = 6.
Next, we apply g to this result:
g(f(0)) = g(6) = 6.
Therefore, (g°f)(0) = 6.
add the numbers in the series 3+11+19+27+.....+395+403.
Answer:
Sum = 10,232
Step-by-step explanation:
The given sequence is Arithmetic Progression.
Arithmetic Progression is a sequence in which every two neighbor digits have equal distances.
For finding the sum of given series firstly we find the number of terms in given series.
For finding the nth term, we use formula
aₙ = a + (n - 1) d
where, aₙ = value of nth term
a = First term
n = number of term
d = difference
Now, In given sequence: 3+11+19+27+.....+395+403
a = 3, d = 8, aₙ = 403
∴ 403 = 3 + (n - 1) × 8
⇒ n = 51
Now, the sum of series is determined by formula,
Sₙ = n ÷ 2 [ a + l]
where l = last term
⇒ Sₙ = 51 ÷ 2 [ 3 + 403]
⇒ Sₙ = 51 × 203
⇒ Sₙ = 10,232
Final answer:
The series 3+11+19+27+.....+395+403 is an arithmetic sequence with a common difference of 8. It has 51 terms, and the sum can be found using the formula Sn = n(a1 + an) / 2, which gives us a sum of 10353.
Explanation:
To add the numbers in the series 3+11+19+27+.....+395+403, we need to recognize that this series is an arithmetic sequence, where each term increases by a common difference. In this case, the common difference is 8 (since 11 - 3 = 8, 19 - 11 = 8, and so on).
First, we need to find the number of terms in the series. We know that an arithmetic series can be expressed as ann = a1 + (n - 1)d, where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms. Plugging in the values we have:
403 = 3 + (n - 1)8
400 = (n - 1)8
n - 1 = 50
n = 51
So there are 51 terms in the series. The sum of an arithmetic series is given by Sn = n(a1 + an) / 2. Plugging in the values we found:
S51 = 51(3 + 403) / 2
S51 = 51(406) / 2
S51 = 10353
Therefore, the sum of the series is 10353.
A square matrix A E Rn is said to be skew-symmetric if A =-A Prove that if A is skew-symmetric, then x'Ax = 0 for all x E R". (Hint The T T T quantity x'Ax is scalar so that (x'Ax) = x'Ax)
Answer:
You can use the given hint as follows:
Step-by-step explanation:
Let [tex]A[/tex] be a square matrix that is a skew-symmetric matrix. Since the matrix [tex]R={\bf x}^{T}A{\bf x}[/tex] is matrix of size [tex]1\times 1[/tex] then it can be identified with an scalar. It is clear that [tex]R=R^{T}[/tex]. Then applying the properties of transposition we have
[tex]({\bf x}^{T}A{\bf x})^{T}=({\bf x}^{T})A^{T}({\bf x}^{T})^{T}={\bf x}^{T}(-A){\bf x}=-{\bf x}^{T}A{\bf x}[/tex]
Then,
[tex]{\bf x}^{T}A{\bf x}+{\bf x}^{T}A{\bf x}=0[/tex]
[tex]2{\bf x}^{T}A{\bf x}=0[/tex]
Then,
[tex]{\bf x}^{T}A{\bf x}=0[/tex]
For all column vector [tex]{\bf x}[/tex] of size [tex]n\times 1[/tex] .
Calculate:
462 grams(g)=____milligrams (mg)
Answer:
462 000mg
Step-by-step explanation:
1gram = 1000milligrams
Hence...462 grams...,
; 462 × 1000 = 462 000mg
462 grams is equal to 462,000 milligrams .
To convert grams ( g ) to milligrams ( mg ), you need to use the following conversion factor:
1 gram ( g ) = 1000 milligrams ( mg )
milligram (mg) is equal to 1/1000 grams (g).
1 mg = (1/1000) g = 0.001 g
The mass m in grams (g) is equal to the mass m in milligrams (mg) divided by 1000:
m(g) = m(mg) / 1000
This means that there are 1000 milligrams in 1 gram. Now, let's use this conversion factor to calculate 462 grams in milligrams:
462 grams * ( 1000 mg / 1 g ) = 462,000 milligrams
So, 462 grams is equal to 462,000 milligrams.
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Va box contains 4 red marbles and 7 green remove 3 at once probability of 3 red
Answer:
0.024
Step-by-step explanation:
Given,
Red marbles = 4,
Green marbles = 7,
Total marbles = 4 +7 = 11,
Ways of choosing 3 marbles =[tex]^{11}C_3[/tex]
Ways of choosing 3 red marble = [tex]^4C_3[/tex]
Hence, the probability of 3 red marble = [tex]\frac{^4C_3}{^{11}C_3}[/tex]
[tex]=\frac{\frac{4!}{3!1!}}{\frac{11!}{3!8!}}[/tex]
[tex]=\frac{4}{165}[/tex]
≈ 0.024
A quadratic function is a function of the form y=ax^2+bx+c where a, b, and c are constants. Given any 3 points in the plane, there is exactly one quadratic function whose graph contains these points. Find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17). Enter the equation below. Function: y = 0
Final answer:
To find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17), we can substitute the x and y values of each point into the standard quadratic function equation y = ax² + bx + c...Therefore, the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17) is y = -x² - 2x - 2.
Explanation:
To find the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17), we can substitute the x and y values of each point into the standard quadratic function equation y = ax^2 + bx + c. This will give us a system of three equations with three variables (a, b, c) that we can solve to find the values of a, b, and c.
Substituting the coordinates (0, -2), we get -2 = a(0)²+ b(0) + c, which simplifies to -2 = c.
Substituting the coordinates (-5, -17), we get -17 = a(-5)² + b(-5) + c, which simplifies to -17 = 25a - 5b + c.
Substituting the coordinates (3, -17), we get -17 = a(3)² + b(3) + c, which simplifies to -17 = 9a + 3b + c.
Since we know that c = -2, we can substitute this value into the other two equations to get -17 = 25a - 5b - 2 and -17 = 9a + 3b - 2.
Simplifying these equations, we get:
25a - 5b = -15 (equation 1)
9a + 3b = -15 (equation 2)
Now we can solve this system of equations using any method such as substitution or elimination to find the values of a and b.
Multiplying equation 1 by 3 and equation 2 by 5, we get:
75a - 15b = -45 (equation 3)
45a + 15b = -75 (equation 4)
Adding equation 3 and equation 4 together, we eliminate the variable b and get:
120a = -120
Dividing both sides by 120, we get a = -1.
Substituting this value of a back into equation 1, we get:
25(-1) - 5b = -15
-25 - 5b = -15
Adding 25 to both sides, we get -5b = 10.
Dividing both sides by -5, we get b = -2.
Therefore, the quadratic function whose graph contains the points (0, -2), (-5, -17), and (3, -17) is y = -x² - 2x - 2.
Let z≥2. What is the remainder of 10^z −1 divided by 4?
Answer:
The remainder is 3.
Step-by-step explanation:
We have to find out,
[tex]10^z-1(mod 4)=?\text{ where }z\geq 2[/tex]
If z = 2,
[tex]10^{2}-1=100-1=99[/tex]
∵ 99 ( mod 4 ) = 3,
Suppose,
[tex](10^{k}-1)(mod 4)=3\forall \text{ k is an integer greater than 2,}[/tex]
Now,
[tex](10^{k+1}-1) ( mod 4)[/tex]
[tex]= (10^k.10 - 10+9)(mod 4)[/tex]
[tex] = 10(mod 4)\times (10^k-1)(mod 4 ) + 9 ( mod 4)[/tex]
[tex]= (2\times 3)(mod 4) + 1[/tex]
[tex]=2+1[/tex]
[tex]=3[/tex]
Hence, our assumption is correct.
The remainder of [tex]10^z -1[/tex] divided by 4 is 3 where, z ≥ 2.
The total number of human genomic characters is 3.5 billion. Express this quantity numerically without using a decimal
Answer:
3,500,000,000
Step-by-step explanation:
The total number of human genomic characters is 3.5 billion.
Expressing this quantity numerically without using a decimal we can write it as ;
3,500,000,000
Use mathematical induction to prove that for each integer n ≥ 4, 5^n ≥ 2 2^n+1 + 100
The given Statement which we have to prove using mathematical induction is
[tex]5^n\geq 2*2^{n+1}+100[/tex]
for , n≥4.
⇒For, n=4
LHS
[tex]=5^4\\\\5*5*5*5\\\\=625\\\\\text{RHS}=2.2^{4+1}+100\\\\=64+100\\\\=164[/tex]
LHS >RHS
Hence this statement is true for, n=4.
⇒Suppose this statement is true for, n=k.
[tex]5^k\geq 2*2^{k+1}+100[/tex]
-------------------------------------------(1)
Now, we will prove that , this statement is true for, n=k+1.
[tex]5^{k+1}\geq 2*2^{k+1+1}+100\\\\5^{k+1}\geq 2^{k+3}+100[/tex]
LHS
[tex]5^{k+1}=5^k*5\\\\5^k*5\geq 5 \times(2*2^{k+1}+100)----\text{Using 1}\\\\5^k*5\geq (3+2) \times(2*2^{k+1}+100)\\\\ 5^k*5\geq 3\times (2^{k+2}+100)+2 \times(2*2^{k+1}+100)\\\\5^k*5\geq 3\times(2^{k+2}+100)+(2^{k+3}+200)\\\\5^{k+1}\geq (2^{k+3}+100)+3\times2^{k+2}+400\\\\5^{k+1}\geq (2^{k+3}+100)+\text{Any number}\\\\5^{k+1}\geq (2^{k+3}+100)[/tex]
Hence this Statement is true for , n=k+1, whenever it is true for, n=k.
Hence Proved.
find the solution of cos(t) * f ` (t) = sin(t)
Answer:
The solution is [tex]f(t)=-\ln \left|\cos \left(t\right)\right|+C[/tex]
Step-by-step explanation:
We know that this ordinary differential equation (ODE) is separable if we can write F(x,y) = f(x)g(y) for some function f(x), g(x).
We can write this ODE in this way
[tex]cos(t) \cdot f'(t)=sin(t)\\f'(t)=\frac{sin(t)}{cos(t)}[/tex]
[tex]\mathrm{If\quad }f^{'} \left(x\right)=g\left(x\right)\mathrm{\quad then\quad }f\left(x\right)=\int g\left(x\right)dx[/tex]
[tex]f(t) =\int\limits{\frac{sin(t)}{cos(t)}} \, dt[/tex]
To solve this integral we need to follow this steps
[tex]\int \frac{\sin \left(t\right)}{\cos \left(t\right)}dt = \\\mathrm{Apply\:u-substitution:}\:u=\cos \left(t\right)\\\int \frac{\sin \left(t\right)}{u}dt \\\mathrm{And \:du=-sin(t)\cdot dt}\\\mathrm{so \>dt=\frac{du}{-sin(t)}}\\\int \frac{\sin \left(t\right)}{u}dt = -\int \frac{1}{u}du[/tex]
[tex]\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)\\-ln|u|\\\mathrm{Substitute\:back}\:u=\cos \left(t\right)\\-\ln \left|\cos \left(t\right)\right|\\[/tex]
Add the constant of integration
[tex]f(t)=-\ln \left|\cos \left(t\right)\right|+C[/tex]
For the final days before the election, the campaign manager has a total of $41,500 to spend on TV and radio campaign advertisements. Each TV ad costs $3000 and is seen by 10,000 voters, while each radio ad costs $500 and is heard by 2000 voters. Ignoring repeated exposures to the same voter, how many TV and radio ads will contact 148,000 voters using the allocated funds?
Answer: There are 9 T.V. and 29 radio ads.
Step-by-step explanation:
Since we have given that
Total amount spend on TV and radio = $41,500
Total number of voters using the allocated funds = 148,000
Let the number of TV be 'x'.
Let the number of radio ads be 'y'.
Cost of each TV = $3000
Cost of each radio ads = $500
Number of voters see T.V. = 10,000
Number of voters use radio = 2000
So, According to question, it becomes,
[tex]3000x+500y=\$41500\implies\ 30x+5y=415\\\\10000x+2000y=148000\implies 10x+2y=148[/tex]
Using the graphing method, we get that
These two lines are intersect at (9,29).
Hence, there are 9 T.V. and 29 radio ads.
Answer: 9 TV ads and 29 radio ads will contact 148,000 voters using the allocated funds .
Step-by-step explanation:
Let x denotes the number of users of TV ads and y denotes the number of radio ads.
Then by considering the given information, we have the foolowing system of equation:-
[tex]\text{Number of voters}\ :10000x+2000y=148000----(1)\\\\\text{Total costs}\ :3000x+500y=41500------(2)[/tex]
Multiply 4 on both sides of equation (2) , we get
[tex]12000x+2000y=166000---------(3)[/tex]
Subtract (1) from (3) , we get
[tex]2000x=18000\\\\\Rightarrow\ x=\dfrac{18000}{2000}=9[/tex]
Put x= 9 , in (2), we get;
[tex]3000(9)+500y=41500\\\\\Rightarrow\ 27000+500y=41500\\\\\Rightarrow\ 500=14500\\\\\Rightarrow\ y=\dfrac{14500}{500}=29[/tex]
Hence, the number of TV ads will be 9 and the number of radio ads will will be 29.
Give the equivalent measure of the ff. use the international metric system. show your solution a. 2.5km = __mm b. 0.05cm= ___mm c. 200.5 g = __kg d 0.03 t = __g e. 30412 sec = __hr
Answer and Explanation:
To find : Convert the given units ?
Solution :
a) 2.5 km to mm
[tex]1\ km = 1000000\ mm[/tex]
[tex]2.5\ km = 2.5\times 1000000\ mm[/tex]
[tex]2.5\ km = 2500000\ mm[/tex]
b) 0.05 cm to mm
[tex]1\ cm = 10\ mm[/tex]
[tex]0.05\ cm =0.05\times 10\ mm[/tex]
[tex]0.05\ cm =0.5\ mm[/tex]
c) 200.5 g to kg
[tex]1\ g = 0.001\ kg[/tex]
[tex]200.5\ g =200.5\times 0.001\ kg[/tex]
[tex]200.5\ g =0.2005\ kg[/tex]
d) 0.03 tone into g
[tex]1\ t =1000000\ g[/tex]
[tex]0.03\ t =0.03\times 1000000\ g[/tex]
[tex]0.03\ t =30000\ g[/tex]
e) 3.0412 sec into hour
[tex]1\ sec =\frac{1}{3600}\ hr[/tex]
[tex]3.0412\ sec =3.0412\times \frac{1}{3600}\ hr[/tex]
[tex]3.0412\ sec =0.000844\ hr[/tex]
Evaluate the function at the given value and simplify.
f(x)=−5x+1
, f(−2)
Question 4 options:
a)
-9
b)
11
c)
-11
d)
9
e)
none
Answer:
The correct option is b.
Step-by-step explanation:
The given function is
[tex]f(x)=-5x+1[/tex]
We need to find the value of f(-2). It means we have to find the value of given function at x=-2.
Substitute x=-2 in the given function to find the value of f(-2).
[tex]f(-2)=-5(-2)+1[/tex]
On simplification we get
[tex]f(-2)=10+1[/tex]
[tex]f(-2)=11[/tex]
The value of f(-2) is 11. Therefore the correct option is b.
In a baseball league consisting of 12 teams, each team plays each of the other teams twice. How many games will be played? There will be games played. Enter your answer in the answer box and then click Check Answer Clear All All parts showing bmt12 0102.ppt bmt12 data-8 30 201.. xlsx data-8 30 201....xlsx Macbook
Answer:
132 games played.
Step-by-step explanation:
Let x be the
We have been given that in a baseball league consisting of 12 teams, each team plays each of the other teams twice.
Since there are 12 teams, so each team will play with [tex](12-1)[/tex] teams except itself.
The total number of games played would be 12 times [tex](12-1)[/tex]:
[tex]\text{The total number of games played}=12(12-1)[/tex]
[tex]\text{The total number of games played}=12(11)[/tex]
[tex]\text{The total number of games played}=132[/tex]
Therefore, there will be 132 games played.
The total number of games that will be played in the baseball league with 12 teams is 66.
Explanation:To find the number of games that will be played in the baseball league, we need to consider that each team plays each of the other teams twice. Since there are 12 teams, each team will play 11 other teams. However, this counts each game twice (once for each team).
So, to find the total number of games, we can use the formula: Total number of games = (Number of teams * Number of teams - Number of teams) / 2.
Substituting the values, we get: Total number of games = (12 * 12 - 12) / 2 = 66.
3 points | Previous Answers LarCalcET6 8.8.012. Ask Your Teacher My Notes Question Part Points Submissions Used Explain why the integral is improper. 0 e7x dx −[infinity] At least one of the limits of integration is not finite. The integrand is not continuous on (-[infinity], 0]. Determine whether it diverges or converges. converges diverges Evaluate the integral if it converges. (If the quantity diverges, enter DIVERGES.)
Answer:
The improper integral converges and [tex]\int_0^{-\infty} e^{7x}dx = -\frac{1}{7}[/tex].
Step-by-step explanation:
First, I assume that the integral in question is
[tex]\int_0^{-\infty} e^{7x}dx[/tex].
Now, the integral is improper because, at least, one of the limits is [tex]\pm\infty[/tex]. We need to recall that an improper integral
[tex]\int_0^{-\infty} f(x)dx[/tex]
converges, by definition, if the following limit exist:
[tex]\lim_{A\rightarrow -\infty} \int_0^A f(x)dx = \int_0^{-\infty} f(x)dx[/tex].
In this particular case we need to study the limit
[tex]\lim_{A\rightarrow -\infty} \int_0^A e^{7x}dx[/tex].
In order to complete this task we calculate the integral [tex]\int_0^A e^{7x}dx[/tex]. Then,
[tex]\int_0^A e^{7x}dx = \frac{e^{7x}}{7}\Big|_0^A = \frac{e^{7A}}{7} - \frac{1}{7}[/tex].
Substituting the above expression into the limit we have
[tex]\lim_{A\rightarrow -\infty} \frac{e^{7A}}{7} - \frac{1}{7} = - \frac{1}{7}[/tex]
because
[tex]\lim_{A\rightarrow -\infty} \frac{e^{7A}}{7}=0[/tex].
EXERCISES 1. For n = 15, 18, 22, 30, and 35, find all positive integers less than n and relatively prime to n.
As per the question,
Note:
''A positive integer is any integer that is greater than zero (0)''. Also, a positive integer is any integer that is a member of the set of natural numbers, i.e., counting numbers; therefore, the positive integers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 25, 26, 27, 28, 29, 30, 31, 32, 33, ...
“Relatively Prime” (also called “co-prime”) numbers are numbers whose HCF is 1. Any consecutive positive integers are co-prime (e.g.: 42 and 43)
Now,
First case: If n = 15
Positive integers (less than n = 15) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14.
Relatively prime are : (1 and 15), (2 and 15), (4 and 15), (7 and 15), (8 and 15), (11 and 15), (13 and 15) and (14 and 15).
Second case: If n = 18
Positive integers (less than n = 18) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 and 17.
Relatively prime are : (1 and 18), (5 and 18), (7 and 18), (11 and 18), (13 and 18) and (17 and 18).
Third case: If n = 22
Positive integers (less than n = 22) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21.
Relatively prime are : (1 and 22), (3 and 22), (5 and 22), (7 and 22), (9 and 22), (13 and 22), (15 and 22), (17 and 22), (19 and 22) and (21 and 22).
Fourth case: If n = 30
Positive integers (less than n = 30) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 and 29.
Relatively prime are : (1 and 30), (7 and 30), (11 and 30), (13 and 30),
(17 and 30), (19 and 30), (23 and 30) and (29 and 30).
Fifth case: If n = 35
Positive integers (less than n = 35) are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33 and 34.
Relatively prime are : (1 and 35), (2 and 35), (3 and 35), (4 and 35), (6 and 35), (8 and 35), (9 and 35), (11 and 35), (12 and 35), (13 and 35), (16 and 35), (17 and 35), (18 and 35), (19 and 35), (22 and 35), (23 and 35), (24 and 35), (26 and 35), (27 and 35), (29 and 35), (31 and 35), (32 and 35), (33 and 35) and (34 and 35).
Question 3. Let f:X --> Y be a function. (a) Recall that for C CY, the inverse image of C is the set f-1(C) = {x E X|f(x) E C}. Let A, B CY. Prove that f-1(ANB) Cf-1(A) n f-1(B). (b) Recall that for D C X, the image of D under f is the set f(D) = {f(x) E YX E X}. Let A, B C X. Prove that f(An B) c f(A)n F(B). Find an example of a function f and sets A and B such that f(ANB) = Ø but f(A) n f(B) + Ø.
Answer:
Step-by-step explanation:
a) We want to prove that [tex]f^{-1}(A\cap B)\subset f^{-1}(A)\cap f^{-1}(B)[/tex]. Then, we can do that proving that every element of [tex]f^{-1}(A\cap B)[/tex] is an element of [tex]f^{-1}(A)\cap f^{-1}(B)[/tex] too.
Then, suppose that [tex]x\in f^{-1}(A\cap B)[/tex]. From the definition of inverse image we know that [tex]f(x)\in A\cap B[/tex], which is equivalent to [tex]f(x)\in A[/tex] and [tex]f(x)\in B[/tex]. But, as [tex] f(x) \in A [/tex] we can affirm that [tex]x\in f^{-1}(A)[/tex] and, because [tex]f(x)\in B[/tex] we have [tex]x\in f^{-1}(B)[/tex].
Therefore, [tex]x\inf^{-1}(A)\cap f^{-1}(B)[/tex].
b) We want to prove that [tex]f(A\cap B) \subset f(A)\cap f(B)[/tex]. Here we will follow the same strategy of the above exercise.
Assume that [tex]y\in f(A\cap B)[/tex]. Then, there exists [tex]x\in A\cap B[/tex] such that [tex]y=f(x)[/tex]. But, as [tex]x\in A\cap B[/tex] we know that [tex]x\in A[/tex] and [tex]x\in B[/tex]. From this, we deduce [tex]f(x)=y\in f(A)[/tex] and [tex]f(x)=y\in f(B)[/tex]. Therefore, [tex]y\in f(A)\cap f(B)[/tex].
c) Consider the constant function [tex]f(x)=1[/tex] for every real number [tex]x[/tex]. Take the sets [tex]A=(0,1)[/tex] and [tex]B=(1,2)[/tex].
Notice that [tex]A\cap B = (0,1)\cap (1,2)[/tex]=Ø, so [tex]f(A\cap B)[/tex]=Ø. But [tex]f(A) = \{1\}[/tex] and [tex]f(B) = \{1\}[/tex], so [tex]f(A)\cap f(B) =\{1\}[/tex].
The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the average mpg for the four models manufactured is 24 mpg and the government standard is 31 mpg. The manufacturer will add a model. What mileage must the new model get so that the manufacturer meets the government requirement?
Answer:
The mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.
Step-by-step explanation:
Consider the provided information.
Here it is given that the average mpg for the four models manufactured is 24 mpg.
The total mpg for the four models = 4 × 24 = 96
The manufacturer will add a model and the government standard is 31 mpg.
This can be written as:
[tex]\frac{96+x}{5}=31[/tex]
[tex]96+x=155[/tex]
[tex]x=155-96[/tex]
[tex]x=59[/tex]
Hence, the mileage must the new model get so that the manufacturer meets the government requirement is 59 mpg.
Final answer:
The new model car must achieve 59 mpg in order for the manufacturer to meet the government requirement of an average of 31 mpg when this model is added to the existing four models that average 24 mpg.
Explanation:
The student has asked what mileage a new model car must get so that the manufacturer meets the government requirement of an average of 31 miles per gallon (mpg). Currently, the average mpg for the manufacturer's four models is 24 mpg.
To calculate the required mpg for the fifth model, we use the formula for the average of a set of numbers, which is the sum of all numbers divided by the number of items. In this case, if x is the mpg the new model needs to achieve, the equation is:
(4 ×24 + x) / 5 = 31
Which simplifies to:
96 + x = 155
Therefore:
x = 155 - 96
x = 59 mpg
The new model will need to have an efficiency of 59 mpg for the manufacturer to meet the Corporate Average Fleet Efficiency (CAFE) standard of 31 mpg.
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. The concession stand at an ice hockey rink had receipts of $6200 from selling a total of 2600 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold? sodas y = hot dogs x =
Answer: 1000 hot dogs and and 1600 sodas were sold.
Step-by-step explanation:
Let x be the number of hot dogs and y be the number of sodas.
Given : The concession stand at an ice hockey rink had receipts of $6200 from selling a total of 2600 sodas and hot dogs.
Each soda sold for $2 and each hot dog sold for $3 .
Then, we have the following system of two linear equations:-
[tex]x+y=2600-----------(1)\\\\3x+2y=6200-----------(2)[/tex]
Multiplying 2 on both sides of (1), we get
[tex]2x+2y=5200------------(3)[/tex]
Now, Eliminate equation (3) from equation (2), we get
[tex]x=1000[/tex]
Put x=1000 in (1), we get
[tex]1000+y=2600\\\\\Rightarrow\ y=2600-1000=1600[/tex]
Hence, 1000 hot dogs and and 1600 sodas were sold.
In order to use a ladder safely, the angle that the ladder forms with the ground should not exceed 70 degree. If you have a ladder that is 16 ft. long, what is the maximum height on the wall of a building that the ladder will safely reach? Round your answer to the nearest thousandth.
Answer:
Maximum safe height can be reached by ladder = 15.03. ft
Step-by-step explanation:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
[tex]Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}[/tex]
[tex]=>Sin70^o\ =\ \dfrac{h}{16\ ft}[/tex]
[tex]=>\ h\ =\ 16\times Sin70^o[/tex]
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Let a, b, c and x elements in the group G. In each of the following solve for x in terms of a, b, and c.
Solve axb =c
Answer:
The answer is [tex]x=a^{-1}cb^{-1}[/tex].
Step-by-step explanation:
First, it is important to recall that the group law is not commutative in general, so we cannot assume it here. In order to solve the exercise we need to remember the axioms of group, specially the existence of the inverse element, i.e., for each element [tex]g\in G[/tex] there exist another element, denoted by [tex]g^{-1}[/tex] such that [tex]gg^{-1}=e[/tex], where [tex]e[/tex] stands for the identity element of G.
So, given the equality [tex] axb=c [/tex] we make a left multiplication by [tex]a^{-1}[/tex] and we obtain:
[tex]a^{-1}axb =a^{-1}c. [/tex]
But, [tex]a^{-1}axb = exb = xb[/tex]. Hence, [tex]xb = a^{-1}c[/tex].
Now, in the equality [tex]xb = a^{-1}c[/tex] we make a right multiplication by [tex]b^{-1}[/tex], and we obtain
[tex] xbb^{-1} = a^{-1}cb^{-1}[/tex].
Recall that [tex]bb^{-1}=e[/tex] and [tex]xe=x[/tex]. Therefore,
[tex]x=a^{-1}cb^{-1}[/tex].
I need help with basic geometry.
Select all the statements that apply to this figure. Please HELp
Answer:
The correct answers are marked.
Step-by-step explanation:
Line k is indicated as perpendicular to RX by the little square at their point of intersection.
Congruence of different line segments will be indicated by marks on them, or by the nature of the geometry containing them (a parallelogram, for instance). There is nothing in this diagram indicating RZ is congruent to GR.
The named points, X, B, V, N, are all shown as being in plane F, so are coplanar.
A plane contains an infinite number of points. In the diagram, there are 5 named points in plane F.
The endpoint of ray RH is point R, which is on line K. However, that is the extent of their intersection. Ray RH heads off in a different direction than line k, so is not part of it.
Segment VN is in plane F; ray RH is not in the plane, but is skew to segment VN. They are not headed in the same direction.
Points R and G are both on line k, so line RG is the same as line k.
In the given figure, line K is perpendicular to RX, points X, B, V, and N are coplanar in plane F, and line RG is the same as line K.
1. Line K is perpendicular to RX:
- This statement is true because there is a right-angle symbol (∟) at the intersection point of lines K and RX, indicating that line K is perpendicular to line RX.
2. RZ is congruent to GR:
- There is no information or markings in the given description that suggest RZ is congruent to GR. Congruence typically requires specific markings or information about the lengths or angles of the line segments, which are not provided in this description.
3. Points X, B, V, and N are coplanar:
- This statement is true. Coplanar points are points that lie in the same plane. In the description, it's mentioned that all these points are in plane F, so they are indeed coplanar.
4. Plane F contains six points:
- This statement is not true. Plane F contains only five named points (R, X, B, V, N) as indicated in the description.
5. Ray RH is part of line K:
- This statement is not true. While the endpoint of ray RH is point R, which is on line K, ray RH heads off in a different direction than line K and does not extend along line K, so it's not considered part of line K.
6. VN is headed the same direction as RH:
- This statement is not true. Segment VN and ray RH are not headed in the same direction. VN is a line segment in plane F, while RH is a ray that extends from point R but does not align with VN.
7. Line RG is the same as line K:
- This statement is true. Both line RG and line K coincide and are represented by the same line in the figure, indicating that they are the same line.
So, statements 1, 3, and 7 are the accurate descriptions of the figure based on the information provided.
To know more about coplanar, refer here:
https://brainly.com/question/17688966
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Where does the term Algorithm from?
Answer:
The term algorithm derives from the title of the Persian and Muslim mathematician of the 9th century Abu Abdullah Muhammad ibn Musa Al-Khwarizmi.
Step-by-step explanation:
The term algorithm derives from the title of the Persian and Muslim mathematician of the 9th century Abu Abdullah Muhammad ibn Musa Al-Khwarizmi. He was a mathematician, astronomer, and geographer during Abbasid Caliphate and he was a researcher at the House of Wisdom in Baghdad.
His systematic method of analyzing linear and quadratic problems resulted in algebra. It is a title derived from all his collection of 830 book title on the topic, "The Compendious Book on Completion and Balancing Calculation."
what equation is graphed in this figure
Answer:
tatho you get the aswer
Step-by-step explanation:
all you have to do is add
Answer:
noice
Step-by-step explanation:
A certain firm has plants A, B, and C producing respectively 35%, 15%, and 50% of the total output. The probabilities of a non-defective product are, respectively, 0.75, 0.95, and 0.85. A customer receives a defective product. What is the probability that it came from plant C?
Answer:
There is a 44.12% probability that the defective product came from C.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
-In your problem, we have:
P(A) is the probability of the customer receiving a defective product. For this probability, we have:
[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]
In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from plant A(we have to consider the probability of plant A being chosen). So:
[tex]P_{1} = 0.35*0.25 = 0.0875[/tex]
[tex]P_{2}[/tex] is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:
[tex]P_{2} = 0.15*0.05 = 0.0075[/tex]
[tex]P_{3}[/tex] is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:
[tex]P_{3} = 0.50*0.15 = 0.075[/tex]
So
[tex]P(A) = 0.0875 + 0.0075 + 0.075 = 0.17[/tex]
P(B) is the probability the product chosen being C, that is 50% = 0.5.
P(A/B) is the probability of the product being defective, knowing that the plant chosen was C. So P(A/B) = 0.15.
So, the probability that the defective piece came from C is:
[tex]P = \frac{0.5*0.15}{0.17} = 0.4412[/tex]
There is a 44.12% probability that the defective product came from C.
Using a sample of 40 patients from a local hospital, researchers measured cholesterol level in an attempt to estimate the mean cholesterol level of U.S. citizens.
Is this study
A. REPRESENTATIVE?
B. NON-REPRESENTATIVE?
Answer:
Non representative
Step-by-step explanation:
A representative sample would be a subset of a population that accurately describes some characteristic from a larger group of people.
A sample of 40 patients from a local hospital is not a big enough sample to estimate the mean cholesterol level of U.S citizens (citizens from an entire country).
Therefore, this sample would be non representative.
A shipment of beach balls with a mean diameter of 28 cm and a standard deviation of 1.3 cm is normally distributed. By how many standard deviations does a beach ball with a diameter of 26.7 cm differ from the mean?
a. 1
b. 1.3
c. 2
d. 3
Answer: a. 1
Step-by-step explanation:
Given : Population mean :[tex]\mu=28\ cm[/tex]
Standard deviation : [tex]\sigma=1.3\ cm[/tex]
Let n be the number of times a beach ball with a diameter of 26.7 cm differ from the mean.
Then, we have
[tex]28-n(1.3)=26.7\\\\\Rightarrow\ 1.3n=28-26.7\\\\\Rightarrow\ 1.3 n=1.3\\\\\Rightarrow\ n=1[/tex]
Hence, a beach ball with a diameter of 26.7 cm is 1 standard deviation differ from the mean.
Find all the values of:
a. (-i)^i
b. (-1)^i
please help we with this complex variable problem.
Answer with Step-by-step explanation:
Part 1)
we know that
[tex]e^{i\theta }=cos(\theta )+isin(\theta )[/tex]
thus [tex]-i=e^{\frac{-i\times (4n-1)\pi }{2}}[/tex]
thus [tex](-i)^i=(e^{\frac{-i\times (4n-1)\pi }{2}})^i\\\\(-i)^i=e^{\frac{-i^2\times (4n-1)\pi }{2}}=e^{\frac{(4n-1)\pi }{2}}\\\\\therefore (-i)^i=e^{\frac{(4n-1)\pi }{2}}[/tex] where 'n' is any integer
Part 2)
We have [tex]-1=e^{(2n+1)\pi }\\\\\therefore (-1)^{i}=(e^{i(2n+1)\pi })^{i}\\\\(-1)^i=(e^{i^2(2n+1)\pi })\\\\(-1)^i=e^{-(2n+1)\pi }[/tex] where 'n' is any integer
Your bag of rice says to mix 1 cup of rice with 2 cups of water. dela requ prov a. What is the ratio of rice to water? refer to your no ncy ratio is id population inimum b. How much water would be needed to mix with 3 cups of rice? by to Sear 64 c. How much water would be need to mix with 1/3 cup of rice? (Hint: How did you do part b for this question? Do the same method for part c!) ed in a different re to se You have 42 tuto se them to ask a st
Answer:
(a) 1:2
(b) 6 cups
(c) [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
(a) Given,
amount of rice mixture contains= 1 cup
amount of water mixture contains= 2 cups
[tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]
[tex]=\ \dfrac{1}{2}[/tex]
So, the ratio of rice to water is 1:2.
(b) Amount of rice in mixture = 3 cups
[tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]
[tex]=>\ \dfrac{1}{2}\ =\ \dfrac{3}{\textrm{amount of water in mixture}}[/tex]
=> amount of water in mixture = 3 x 2
= 6 cups
(c) [tex]\textrm{amount of rice in mixture}\ =\dfrac{1}{3}[/tex]
[tex]\textrm{So, the ratio of rice to water}\ =\ \dfrac{\textrm{amount of rice in mixturte}}{\textrm{amount of water in mixture}}[/tex]
[tex]=>\ \dfrac{1}{2}\ =\ \dfrac{\dfrac{1}{3}}{\textrm{amount of water in mixture}}[/tex]
[tex]=>\textrm{amount of water in mixture}\ =\ \dfrac{2}{3}[/tex]
So, the amount of water in the mixture will be [tex]\dfrac{2}{3}[/tex] cup.
Let A 10,1,2,3,4,5,61, let B 0,1,2,3,4,5,6,7,81, and let R be the relation from A to B given by "the greatest common divisor of a and b is 2." [Note: "greatest common divisor" is sometimes called "highest common factor".] List the elements of R.
Answer:
R={(10,2),(10,4),(10,6),(2,2),(2,4),(2,6),(4,2),(4,6)}
Step-by-step explanation:
We are given that
A={10,1,2,3,4,5,61}
B={0,1,2,3,4,5,6,7,81}
We are given that R be the relation from A to B
R={gcd(a,b)=2,a[tex]\inA,b\inB[/tex]}
Gcd=Greatest common divisor of a and b.
We have to find the elements in R
(10,2)=2,(10,4)=2,(10,6)=2
(2,2)=2,(2,4)=2,(2,6)=2
(4,2)=2,(4,6)=2
Therefore, R={(10,2),(10,4),(10,6),(2,2),(2,4),(2,6),(4,2),(4,6)}
What is the x-intercept of the linear equation y = 4x – 4
Answer: (1,0)
Step-by-step explanation: What is the x-intercept of the linear equation y = 4x – 4?
y = 4x - 4
x-intercept ⇒ y = 0
which means that we need to substitute the y by 0.
0 = 4x-4
4x = 4
x = 1
As it is a linear equation, 1st degree, there is only one point.
This way, the linear y = 4x - 4 intercept x on point (1,0)