Answer: y = 3x - 2
Step-by-step explanation:
gradient = (4 - 1)/(2 - 1) = 3/1 = 3
y = 3x + c needs to work for both points
Substitute (1,1) into equation
1 = 3 x 1 + c
c = 1 - 3 = -2
y = 3x - 2
What is the inverse of
F(x) =5x/3+ 5
The inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
How to determine the inverse?The function is given as:
f(x) = 5x/3 + 5
Rewrite as:
y = 5x/3 + 5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
x - 5 = 5y/3
Multiply through by 3
3x - 15 = 5y
Divide through by 5
y = 3x/5 - 3
Express as inverse function
f-1(x) = 3x/5 - 3
Hence, the inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
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Work out the reciprocal of 0.0005. Give your answer in standard form. 7 Work out the reciprocal of 0.0005 . Give your answer in standard form .
Answer:
that's all I could do. hope it helps.
good day.
How many three-letter "words" can be made from 7 different letters "FGHIJKL" if...
a) Repetition of letters is allowed?
b) Repetition of letters is not allowed?
Answer:
343
Step-by-step explanation:
How many three-letter ”words” can be made from 7 letters FGHIJKL” if repetition of letters (a) is allowed? (b) is not allowed? Solution: (a) If repetition is allowed each letter can be any of the 7. So number ways is 7 × 7 × 7=73 = 343
Answer: See below
Step-by-step explanation:
Given:
The letters FGHIJKL
To find:
The number of three letter words can be formed if repetition is allowed (or) if repetition is not allowed
[tex]$$(a) If repetition is allowed:Total no of three letter words can be made$$=7_{C 1} x 7_{C 1} x 7_{C 1}=7^{3}=343$$(b) If repetitions is not allowed :Total no of three letter words can be made without repetition is $$\begin{gathered}=7_{C 1} \times 6_{C 1} \times 5_{C 1} \\=7 x 6 \times 5=210\end{gathered}$$[/tex]
Taylor earned the following scores on her first ten quizzes. What would she need to earn on the eleventh test in order to have a mean score of 87? 78, 92, 98, 87, 86, 72, 92, 81, 86, 92
A mean is an arithmetic average of a set of observations. The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The score earned by Taylor in her first 10 test are 78, 92, 98, 87, 86, 72, 92, 81, 86, 92. Also, she wants the average to be 87, therefore, we can write,
(78 + 92 + 98 + 87 + 86 + 72 + 92 + 81 + 86 + 92 + x)/11 = 87
864 + x = 957
x = 93
Hence, The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
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Can someone please help me
Answer:
Number 4
Standard form - Not sure if right
y = − 0.2734375x^2 − 1.09375x +11.40625
Factored form - Not sure if right
y= 0.0390625 (−7x^2 −28x+292)
Number 5
Either form of the equation other than standard form
Vertex form : y = −(x +3)^2 + 25
Vertex of the parabola
(-3,25)
X and Y intercepts
x-intercept(s): (2,0) ,(−8,0)
y-intercept(s): (0,16)
Barn Yard Inc. is a wholesaler that stocks engine components and tests equipment for the commercial aircraft industry. A new customer has placed an order for eight high-bypass turbine engines, which increase fuel economy. The variable cost is $1.6 million per unit, and the credit price is $1.725 million each. Credit is extended for one period, and based on historical experience, payment for about one out of every 200 such orders is never collected. The required return is 1.8% per period.Suppose that customers who don’t default become repeat customers and place the same order every period forever. Further assume that repeat customers never default.
The NPV is positive, therefore, this order can be placed.
How to calculate the NPV?The calculation of probability of default will be:
= 1 / 200 = 0.005
We use NPV formula to find out whether the order should be filled or not
NPV = -Variable cost per unit +[(1-π)(price of equipment/1+percentage of return)]
= -$1.6 million +[(1-0.005)($1.725m/1.018)]
= -$1.6m + $1.6860
= 0.0860 million
As NPV is positive this order can be placed.
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Problem
A [tex]prime\left trio[/tex] is a collection of three prime numbers [tex]\{p, q, r\}[/tex] in arithmetic progression, with common difference [tex]q-p=r-q[/tex]. For example, the prime trio [tex]\{3, 5, 7\}[/tex] has common difference 2.
Prove that there is no prime trio with common difference 70.
P.S. I want actual proof.
Answer:
Proof below
Step-by-step explanation:
General outlineLemma regarding remainders of non-small primes divided by 6Check [tex]p=2[/tex] and [tex]p=3[/tex] directlyProof the rest by contradictionLemmaIf [tex]p[/tex] is prime such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then [tex]p[/tex] divided by 6 has remainder of 1 or 5.
Case 1: p/6 has remainder 0, 2, or 4.
Then there exists some natural number [tex]n[/tex] such that either [tex]p=6n[/tex], [tex]p=6n+2[/tex], or [tex]p=6n+4[/tex]. However,
if [tex]p=6n[/tex], then [tex]p=2*3n[/tex],if [tex]p=6n+2[/tex], then [tex]p=2*(3n+1)[/tex], and if [tex]p=6n+4[/tex], then [tex]p=2*(3n+2)[/tex].By definition of divisibility, [tex]p[/tex] is divisible by 2. Since [tex]p \neq2[/tex], [tex]p[/tex] cannot be prime. This contradiction implies [tex]p[/tex] cannot have a remainder of 0, 2, or 4 when divided by 6.
Case 2: p/6 has remainder 3.
Then there exists some natural number [tex]n[/tex] such that [tex]p=6n+3[/tex]. However, if [tex]p=6n+3[/tex], then [tex]p=3*(2n+1)[/tex], so [tex]p[/tex] is divisible by 3. Since [tex]p \neq 3[/tex], [tex]p[/tex] is not prime. This contradiction implies [tex]p[/tex] cannot have a remainder of 3 when divided by 6.
Therefore, if [tex]p[/tex] is a prime number such that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex], then when divided by 6, [tex]p[/tex] must have a remainder of 1 or 5.
Main proof of no prime trio with common difference of 70.Check p=2
Consider [tex]p=2[/tex]. Then [tex]q=2+70=72[/tex]. However, [tex]72=2*36[/tex], so [tex]q[/tex] is not prime. Hence, [tex]p \neq2[/tex].
Check p=3
Consider [tex]p=3[/tex]. Then [tex]q=3+70=73[/tex], and [tex]r=73+70=143[/tex]. However, [tex]143=11*13[/tex], so [tex]r[/tex] is not prime. Hence, [tex]p \neq 3[/tex].
So, thus far, we've proven that if there is a prime trio with a common difference of 70, that [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].
Proof of the rest of primes by contradiction
By way of contradiction, assume that there does exist some prime trio [tex]\{ p,q,r \}[/tex] such that [tex]q-p=r-q=70[/tex], and [tex]p \neq2[/tex] and [tex]p \neq 3[/tex].
Then, by the Lemma proven earlier, when [tex]p[/tex] is divided by 6, it must have a remainder of 1 or 5.
Case 1: p/6 has remainder 5
Assume that [tex]p[/tex] has remainder 5 when divided by 6. Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+5[/tex].
[tex]q=p+70\\q=(6n+5)+70\\q=6n+75\\q=3*(2n+25)[/tex]
Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), then [tex]q[/tex] is divisible by 3.
Since [tex]p[/tex] is prime, [tex]0 < p[/tex], which implies [tex]0+70 < p+70[/tex]
Since [tex]q=p+70[/tex], [tex]70 < q[/tex], so [tex]q[/tex] cannot equal 3. Since [tex]q[/tex] is divisible by 3, but [tex]q \neq 3[/tex], [tex]q[/tex] is not prime, which is a contradiction to the existence of this prime trio.
Therefore, either [tex]p[/tex] cannot have a remainder of 5 when divided by 6, or the prime trio does not exist.
Case 2: p/6 has remainder 1
Assume that [tex]p[/tex] has remainder 1 when divided by 6. Then, there exists some natural number [tex]n[/tex], such that [tex]p=6n+1[/tex].
[tex]q=p+70\\q=(6n+1)+70\\r=q+70\\r=((6n+1)+70)+70\\r=6n+141\\r=3*(2n+47)[/tex]
Since [tex]n[/tex] was a natural number, and the natural numbers are closed over multiplication and addition (meaning, multiplying and adding more natural numbers results in another natural number), [tex]r[/tex] is divisible by 3.
Since [tex]q[/tex] is prime, [tex]0 < q[/tex], implying [tex]0 +70 < q+70[/tex].
Since [tex]r=q+70[/tex], then [tex]70 < r[/tex]. Therefore, [tex]r\neq 3[/tex].
Since [tex]r[/tex] is divisible by 3, but [tex]r\neq 3[/tex], [tex]r[/tex] is not prime, which is a contradiction to the existence of this prime trio (with a common difference of 70). Therefore, either [tex]p[/tex] cannot have a remainder of 1 when divided by 6, or the prime trio does not exist.
Since [tex]p[/tex] was prime, by our lemma [tex]p[/tex] must have either a remainder of 1 or 5. Since both remainder possibilities resulted in a contradiction, our contradiction assumption is false, so there cannot exist a prime trio such that their common difference is 70.
A line passes through the point (8, -1) and has a slope of
Write an equation in slope-intercept form for this line.
The equation in slope intercept form is y = - 1 / 4 x + 1
How to find the slope intercept equation?Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = - 1 / 4
it passes through (8, -1)
Hen e,
-1 = - 1 / 4 (8) + b
-1 = - 2 + b
b = -1 + 2
b = 1
Therefore,
y = - 1 / 4 x + 1
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Given: 1.1 1.2 1.3 f(x) = 8 +4 x-8
Write down the domain and range off.
Write down the equations of the asympotes of f
Sketch the graph of f clearly showing the intercepts with the axes and the asymptotes.
Answer:
Did you mean " f(x)=8+4^{x-8} ? " The function you entered was linear, meaning there would be no asymptote.
D: (-∞, +∞)
R: (8, +∞)
Horizontal asymptote at y=8
No vertical asymptote
Divide. Write the quotient in lowest terms.
Answer:
11/12
Step-by-step explanation:
2 3/4 ÷ 3
11/4 ÷ 3
11/4 × 1/3
11/12
Answer:
Hello! The answer is 11/12.
Step-by-step explanation:
Convert improper fractions:
[tex]2\frac{3}{4} \\= \frac{11}{4}[/tex]
Change 3 to its reciprocal:
[tex]\frac{1}{3}[/tex]
Multiply:
[tex]\frac{11}{4} * \frac{1}{3} \\= 11/12[/tex]
Order the quotients of these expressions from least to greatest.
42.6 ÷ 70
42.6 ÷ 0.7
426 ÷ 70
42.6 ÷ 0.07
Translate and solve: the product of
p
and
−
2.5
is
4.8
Answer:
p = 7.3
Step-by-step explanation:
Equation: p - 2.5 = 4.8
add 2.5 to both sides:
P - 2.5 + 2.5 = 4.8 + 2.5
simplify
P = 7.3
hope that helps! :)
Sandy borrows $1250 from the bank. The loan terms is 18 months with 5% annual interest. How much interest will she pay? How much will she pay back in all?
Answer:
Step-by-step explanation:
1250x0.05x1.5=93.75
93.75 is the interest
1343.75 is the total ammount.
Write the augmented matrix of the system of equations given below. (10 points)
−2 + 2 − = −13
−3 − + = 7
− + 3 − 2 = 0
The augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
How to determine the augmented matrix?The system of equations is given as:
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
Remove the variables x, y and z
-2 2 -1 13
-3 -1 1 7
-1 3 -2 0
Express as matrix
[tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
Hence, the augmented matrix of the system of equations is [tex]\left[\begin{array}{ccc}-2&2&-1\\-3&-1&1\\-1&3&-2\end{array}\right] \left[\begin{array}{c}13&7\\0\end{array}\right][/tex]
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Complete question
Write the augmented matrix of the system of equations given below. (10 points)
-2x + 2y - z = 13
-3x - y + z = 7
-x + 3y - 2z = 0
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe some answers are correct. Thank you!
The approximate 95 % confidence interval for p is found by the formula
p^ ± Z∝/2 √p^q^/n
The sample size n can be found by the
The formula
n= (Z∝/2)² p^q^/e²
The approximate 95 % confidence interval for p is 0.165; 0.243
This indicates 95 % confidence interval level.
A sample of 6239 nonprofits should be surveyed
Solution
Part a:
Sample Proportion p^= 84/412= 0.2038 ≅ 0.204
q^ = 1-p^= 1.0 -0.204= 0.796
The degree of confidence is 95% so z∝/2= 1.96
Putting the values
p^ ± Z∝/2 √p^q^/n
0.204 ± 1.96 √0.204(0.796)/ 412
0.204 ± 0.0389
0.1650 ; 0.2429
0.165; 0.243
The approximate 95 % confidence interval for p is 0.165; 0.243
Part B
This indicates 95 % confidence interval level.
Part C
With ± 0.01 of 0.95 Confidence interval gives range 0.94 to 0.96
For 0.96 interval Z∝/2 = 2.054
For 0.94 interval Z∝/2 = 1.8808
and error e= 0.01
For solving n the formula is
n= (Z∝/2)² p^q^/e²
and e= 0.01
Putting the values
n= 1.96²(0.204)(0.796)/ 0.01²
n= 6238.1437≅ 6238.14
A sample of 6239 nonprofits should be surveyed.
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can you please help me with this question? thanks!
Answer:
Step 2
Step-by-step explanation:
In step 1, Gary had the right idea of multiplying both sides by 4 to eliminate the denominator, but in step 2, Gary makes a mistake since e should equal 10 not 8. 2.5 * 4 = 10 not 8
Answer:
B) Step 2
Step-by-step explanation:
Gary's mistake occurs in Step 2. He was right to multiply both sides of the equation by 4 to find e, but his error is in the multiplication of 2.5*4. 2.5*4 = 10, not 8.
A tennis ball can in the shape of a right circular cylinder holds four tennis balls snugly. If the radius of a tennis ball is 3.5 cm, what percentage of the can is not occupied by tennis balls?
Answer:
about 33.3%
Step-by-step explanation:
The fraction of space not occupied will be the same as the unoccupied fraction of a cylinder of the same height and diameter as a sphere.
Volume of a cylinderThe volume of a cylinder of diameter d and height d will be ...
V = πr²h = π(d/2)²(d) = (π/4)d³
Volume of a sphereThe volume of a sphere of diameter d is ...
V = 4/3πr³ = 4/3π(d/2)³ = (π/6)d³
Unoccupied spaceThe fraction of space that is occupied is ...
occupied space = (sphere volume)/(cylinder volume)
occupied space = ((π/6)d³) / ((π/4)d³) = 4/6 = 2/3
The fraction of unoccupied space is ...
unoccupied fraction = 1 -2/3 = 1/3
unoccupied fraction ≈ 33.3%
Answer:
Putangina okay
Step-by-step explanation:
#CarryOnLearning
What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
John had $24,500 to invest. He divided the money into three different accounts. At the end of the first year he had made a total of $1,300 in interest between the three accounts. If the first account earned 4% interest on its original amount for the year, the second account earned 5.5% interest on its original amount for the year, and the third account earned 6% interest on its original amount for the year. Also, the amount of money in the first account was 4 times the amount in the second account. How much had he originally placed in each account?
Answer:
The method of matrixes that would be used for this question is Gaussian Elimination.
Step-by-step explanation:
Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:
4x + 5.5y + 6z = 1,300
x + y + z = 24,500
4x = y
We can then use Gaussian Elimination to solve for x, y, and z.
What will sue pay for 18 oranges if the cost 0.49 for 6 show the process
Answer:
[tex]\huge\boxed{\sf \$ \ 1.47}[/tex]
Step-by-step explanation:
Given that,6 oranges = $0.49
Multiply 3 to both sides
6×3 oranges = $0.49 × 3
18 oranges = $1.47
[tex]\rule[226]{225}{2}[/tex]
If n + 2, 5, and 9 represent the lengths of the sides of a triangle then < n
Answer:
n>2 (see below)
Step-by-step explanation:
Triangle side rule says n+2 + 5 must be greater than 9
n+2 +5 > 9
n > 2
(but it must be less than 12 o/w 5 + 9 will not be greater than n+2)
What fraction of this shape is shaded?
Time
Running
Give your answer in its simplest form.
Write this in logarithm form √x = y
The logarithmic form of √x = y is ㏒ₓy = 1/2
How to determine the logarithmic formWe have, logarithmic form as;
㏒ₓ n = bⁿGiven √x = y
Convert the square root to power of 1/2 as that is what it represents, we get
x^1/2 = y
Then compare with the universal logarithmic form, we have
㏒ₓy = 1/2
Thus, the logarithmic form of √x = y is ㏒ₓy = 1/2
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Please help! Consider the following subset of the real number line. How can this set be expressed using inequalities?
Answer:
-2 ≤ x ≤10
Step-by-step explanation:
Notice that x can never be less than -2 and can never exceed.
-2 and 10 are all inclusive thus the last answer is not correct as it tries to leave them out
A fixed deposit receipt initiallypurchased for #1,500,000 for 4years has a maturity value of #1,300,000. What is the simple interest rate per year?
Answer:
11 3/13% per annum
Step-by-step explanation:
to find rate= 100×simple interest ÷ (principal ×time)
simple interest=total amount - principal
=1,500,000-1,300,000
=200,000
=200,000 ×100÷ 1,300,000×4
=3 11/13% per annum
Find the product of the given polynomials
(5r+8-6r)(4+2r-7)
A.2r^2+13r-24
B.-2r^2-24r+19
C.-2r^2+19r-24
D.2r^2+19r+24
Answer:
C
Step-by-step explanation:
(5r + 8 - 6r)(4 + 2r - 7) ← collect like terms inside each parenthesis
= (8 - r)(2r - 3)
each term in the second factor is multiplied by each term in the first factor.
8(2r - 3) - r(2r - 3) ← distribute parenthesis
= 16r - 24 - 2r² + 3r ← collect like terms
= - 2r² + 19r - 24
Which linear inequality is represented by the graph?
Answer:
y>2/3+3
Step-by-step explanation:
Answer:
y<2/3x+3
Step-by-step explanation:
1. Find the slope, the slope is 2/3
2. Find the y-intercept, the y intercept is 3
3. Make an linear equation out of it, y=2/3x+3
4. Dotted or solid? Its dotted which means the answer has to be greater or less than, not equal or less than or equal or greater than
5. Test you have 2 answer choices y<2/3x+3 or y>2/3x+3, input the origin (0,0)
0<2/3(0)+3, 0<3 which is true
0>2/3(0)+3 0>3 which is false
So y<2/3x+3 is the right answer. :)
if anyone knows how to answer this do so pleass
Answer:
x = 4.08
Step-by-step explanation:
As we now, from Trigonometric Identities
that [tex]tan(\alpha )=\frac{Opposite}{Adjacent}[/tex]So for our Problem , [tex]\alpha =27[/tex] , [tex]Opposite=x[/tex] , [tex]Adjacent = 8[/tex]
by substituting , then [tex]tan(27)=\frac{x}{8}[/tex]
by multiplying both sides by 8 , then [tex]x=8tan(27)=4.0762=4.08[/tex]
Find the area of the triangle if b = 8 inches and h = 4 inches
The area of triangle is 16 square inches.
what is Area of Triangle?Area of triangle is half times the product of base and height.
i.e., A-= 1/2 *b *h
Given:
b= 8 inches, h= 4 inches
Now, Area of triangle
= 1/2*b*h
= 1/2 * 8 *4
=1/2*32
=16.
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c. Divide 45 into three parts which are in A.P. Such that the pr oduct of last two is 300.
Find f(x-4) if f(x)=-x+2. f(x-4)
Answer:
= -x+6
Step-by-step explanation:
we can simply substitute (x-4) in x place because when we say function of x , we are basically saying when we substitute a given value in the place of x we will find a given y.so for example if we have a question f(4), we can simply plug 4 to -x +2 so we will find y or f(x) = -2.
so the answer for the above question will be f(x)= -x +6.