a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.
b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
How is the future value determined?The future value can be determined using an online finance calculator.
Data and Calculations:
a) Compounded Semiannually:Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Semi-Annually
Time (t in years): 8 years
Result:
A = $11,949.50
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,244.94
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,704.56(1 + 0.04/2)(2)(8)
A = 8,704.56(1 + 0.02)(16)
A = $11,949.50
b) Compounded Continuously:Using the formula A = Pert
Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Continuously
Time (t in years): 8 years
Result:
A = $11,987.29
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,282.73
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A, using the mathematical constant, e = 2.71828
A = Pert
A = 8,704.56(2.71828)(0.04)(8)
A = $11,987.29
Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
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f(1)=−6
f(2)=−4
f(n)=f(n−2)+f(n−1)
f(n)=?
The nth term of the sequence is 2n - 8
Equation of a functionThe nth term of an arithmetic progression is expressed as;
Tn = a + (n - 1)d
where
a is the first term
d is the common difference
n is the number of terms
Given the following parameters
a = f(1)=−6
f(2) = −4
Determine the common difference
d = f(2) - f(1)
d = -4 - (-6)
d = -4 + 6
d = 2
Determine the nth term of the sequence
Tn = -6 + (n -1)(2)
Tn = -6+2n-2
Tn = 2n - 8
Hence the nth term of the sequence is 2n - 8
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By definition, we have
[tex]f(n) = f(n - 1) + f(n - 2)[/tex]
so that by substitution,
[tex]f(n-1) = f(n-2) + f(n-3) \implies f(n) = 2f(n-2) + f(n-3)[/tex]
[tex]f(n-2) = f(n-3) + f(n-4) \implies f(n) = 3f(n-3) + 2f(n-4)[/tex]
[tex]f(n-3) = f(n-4) + f(n-5) \implies f(n) = 5f(n-4) + 3f(n-5)[/tex]
[tex]f(n-4) = f(n-5) + f(n-6) \implies f(n) = 8f(n-5) + 5f(n-6)[/tex]
and so on.
Recall the Fibonacci sequence [tex]F(n)[/tex], whose first several terms for [tex]n\ge1[/tex] are
[tex]\{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, \ldots\}[/tex]
Let [tex]F_n[/tex] denote the [tex]n[/tex]-th Fibonacci number. Notice that the coefficients in each successive equation form at least a part of this sequence.
[tex]f(n) = f(n-1) + f(n-2) = F_2f(n-1) + F_1 f(n-2)[/tex]
[tex]f(n) = 2f(n-2) + f(n-3) = F_3 f(n-2) + F_2 f(n-3)[/tex]
[tex]f(n) = 3f(n-3) + 2f(n-4) = F_4 f(n-3) + F_3 f(n-4)[/tex]
[tex]f(n) = 5f(n-4) + 3f(n-5) = F_5 f(n-4) + F_4 f(n-5)[/tex]
[tex]f(n) = 8f(n-5) + 5f(n-6) = F_6 f(n-5) + F_5 f(n-6)[/tex]
and so on. After [tex]k[/tex] iterations of substituting, we would end up with
[tex]f(n) = F_{k+1} f(n - k) + F_k f(n - (k+1))[/tex]
so that after [tex]k=n-2[/tex] iterations,
[tex]f(n) = F_{(n-2)+1} f(n - (n-2)) + F_{n-2} f(n - ((n-2)+1)) \\\\ f(n) = f(2) F_{n-1} + f(1) F_{n-2} \\\\ \boxed{f(n) = -4 F_{n-1} - 6 F_{n-2}}[/tex]
What is the ordered pair of X' after point X (3, 4) is rotated 180°?
OX' (3,-4)
OX' (-3,-4)
OX' (-4, 3)
OX' (-4,-3)
Fraction how do you make 0.475 a simple fraction
Answer: 19/40
Step-by-step explanation:
First Write 0.475 as 0.4751Multiply both numerator and denominator by 10 for every number after the decimal point0.475 × 10001 × 1000 = 4751000. Reducing the fraction gives The answer
Let g(x)= 18 - 3x
Find g-¹ (0). Final answer is just a number.
Answer:
g(0)⁻¹ = 6
Step-by-step explanation:
First, you must find the inverse of the function. Remember, another way of representing g(x) is with "y". To find the inverse, you must swap the positions of the "x" and "y" variables in the equation. Then, you must rearrange the equation and isolate "y".
g(x) = 18 - 3x <----- Original function
y = 18 - 3x <----- Plug "y" in for g(x)
x = 18 - 3y <----- Swap the positions of "x" and "y"
x + 3y = 18 <----- Add 3y to both sides
3y = 18 - x <----- Subtract "x" from both sides
y = (18 - x) / 3 <----- Divide both sides by 3
y = 6 - (1/3)x <----- Divide both terms by 3
Now that we have the inverse function, we need to plug x = 0 into the equation and solve for the output. In the inverse function, "y" is represented by the symbol g(x)⁻¹.
g(x)⁻¹ = 6 - (1/3)x <----- Inverse function
g(0)⁻¹ = 6 - (1/3)(0) <----- Plug 0 in for "x"
g(0)⁻¹ = 6 - 0 <----- Multiply 1/3 and 0
g(0)⁻¹ = 6 <----- Subtract
Ryan obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. His loan is for $17,100 for 54 days. Assume 1/365 each day is of a year. Answer each part below.
Do not round any intermediate computations, and round your final answers to the nearest cent.
(a) Find the interest that will be owed after 54 days. $ (b) Assuming Ryan doesn't make any payments, find the amount owed after 54 days.
well, with the assumption that a year has 365 days, that means one day is really just 1/365th of a year, so then 54 days will be 54/365 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$17100\\ r=rate\to 9.65\%\to \frac{9.65}{100}\dotfill &0.0965\\ t=years\dotfill &\frac{54}{365} \end{cases} \\\\\\ I = (17100)(0.0965)(\frac{54}{365})\implies \stackrel{\textit{interest owed}}{I\approx 244.13}~\hfill \underset{amount~owed}{\stackrel{17100~~ + ~~244.13}{\approx 17344.13}}[/tex]
In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, at which point will the particle stop?
The particle will stop at D.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, then
Number of sides = 5
Let x be the one complete revolution.
5 x = 725
x = 145
Now, 145 - 2 = 143
Hence, it will stop at D which is 2 less than A.
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Twenty years ago, 51% of parents of children in high school felt it was a
serious problem that high school students were not being taught
enough math and science. A recent survey found that 232 of 700
parents of children in high school felt it was a serious problem that high
school students were not being taught enough math and science. Do
parents feel differently today than they did twenty years ago? Use the
α = 0.1 level of significance
No the parents do not feel differently as they used to feel twenty years ago
Given :-
Po: p=0.46
Pa: p NE 0.46
alpha=0.01
Test statistic is one sample proportion [tex]z=(phat-p)/\sqrt{{ {0.46)(0.54)/800}}[/tex]
Critical value z> |2.576|
z=0.025/0.0176
=1.418
This is a p-value of 0.078
Fail to reject Po and insufficient evidence to support the claim that parents feel differently.
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I honestly need help with these
9. The curve passes through the point (-1, -3), which means
[tex]-3 = a(-1) + \dfrac b{-1} \implies a + b = 3[/tex]
Compute the derivative.
[tex]y = ax + \dfrac bx \implies \dfrac{dy}{dx} = a - \dfrac b{x^2}[/tex]
At the given point, the gradient is -7 so that
[tex]-7 = a - \dfrac b{(-1)^2} \implies a-b = -7[/tex]
Eliminating [tex]b[/tex], we find
[tex](a+b) + (a-b) = 3+(-7) \implies 2a = -4 \implies \boxed{a=-2}[/tex]
Solve for [tex]b[/tex].
[tex]a+b=3 \implies b=3-a \implies \boxed{b = 5}[/tex]
10. Compute the derivative.
[tex]y = \dfrac{x^3}3 - \dfrac{5x^2}2 + 6x - 1 \implies \dfrac{dy}{dx} = x^2 - 5x + 6[/tex]
Solve for [tex]x[/tex] when the gradient is 2.
[tex]x^2 - 5x + 6 = 2[/tex]
[tex]x^2 - 5x + 4 = 0[/tex]
[tex](x - 1) (x - 4) = 0[/tex]
[tex]\implies x=1 \text{ or } x=4[/tex]
Evaluate [tex]y[/tex] at each of these.
[tex]\boxed{x=1} \implies y = \dfrac{1^3}3 - \dfrac{5\cdot1^2}2 + 6\cdot1 - 1 = \boxed{y = \dfrac{17}6}[/tex]
[tex]\boxed{x = 4} \implies y = \dfrac{4^3}3 - \dfrac{5\cdot4^2}2 + 6\cdot4 - 1 \implies \boxed{y = \dfrac{13}3}[/tex]
11. a. Solve for [tex]x[/tex] where both curves meet.
[tex]\dfrac{x^3}3 - 2x^2 - 8x + 5 = x + 5[/tex]
[tex]\dfrac{x^3}3 - 2x^2 - 9x = 0[/tex]
[tex]\dfrac x3 (x^2 - 6x - 27) = 0[/tex]
[tex]\dfrac x3 (x - 9) (x + 3) = 0[/tex]
[tex]\implies x = 0 \text{ or }x = 9 \text{ or } x = -3[/tex]
Evaluate [tex]y[/tex] at each of these.
[tex]A:~~~~ \boxed{x=0} \implies y=0+5 \implies \boxed{y=5}[/tex]
[tex]B:~~~~ \boxed{x=9} \implies y=9+5 \implies \boxed{y=14}[/tex]
[tex]C:~~~~ \boxed{x=-3} \implies y=-3+5 \implies \boxed{y=2}[/tex]
11. b. Compute the derivative for the curve.
[tex]y = \dfrac{x^3}3 - 2x^2 - 8x + 5 \implies \dfrac{dy}{dx} = x^2 - 4x - 8[/tex]
Evaluate the derivative at the [tex]x[/tex]-coordinates of A, B, and C.
[tex]A: ~~~~ x=0 \implies \dfrac{dy}{dx} = 0^2-4\cdot0-8 \implies \boxed{\dfrac{dy}{dx} = -8}[/tex]
[tex]B:~~~~ x=9 \implies \dfrac{dy}{dx} = 9^2-4\cdot9-8 \implies \boxed{\dfrac{dy}{dx} = 37}[/tex]
[tex]C:~~~~ x=-3 \implies \dfrac{dy}{dx} = (-3)^2-4\cdot(-3)-8 \implies \boxed{\dfrac{dy}{dx} = 13}[/tex]
12. a. Compute the derivative.
[tex]y = 4x^3 + 3x^2 - 6x - 1 \implies \boxed{\dfrac{dy}{dx} = 12x^2 + 6x - 6}[/tex]
12. b. By completing the square, we have
[tex]12x^2 + 6x - 6 = 12 \left(x^2 + \dfrac x2\right) - 6 \\\\ ~~~~~~~~ = 12 \left(x^2 + \dfrac x2 + \dfrac1{4^2}\right) - 6 - \dfrac{12}{4^2} \\\\ ~~~~~~~~ = 12 \left(x + \dfrac14\right)^2 - \dfrac{27}4[/tex]
so that
[tex]\dfrac{dy}{dx} = 12 \left(x + \dfrac14\right)^2 - \dfrac{27}4 \ge 0 \\\\ ~~~~ \implies 12 \left(x + \dfrac14\right)^2 \ge \dfrac{27}4 \\\\ ~~~~ \implies \left(x + \dfrac14\right)^2 \ge \dfrac{27}{48} = \dfrac9{16} \\\\ ~~~~ \implies \left|x + \dfrac14\right| \ge \sqrt{\dfrac9{16}} = \dfrac34 \\\\ ~~~~ \implies x+\dfrac14 \ge \dfrac34 \text{ or } -\left(x+\dfrac14\right) \ge \dfrac34 \\\\ ~~~~ \implies \boxed{x \ge \dfrac12 \text{ or } x \le -1}[/tex]
13. a. Compute the derivative.
[tex]y = x^3 + x^2 - 16x - 16 \implies \boxed{\dfrac{dy}{dx} = 3x^2 - 2x - 16}[/tex]
13. b. Complete the square.
[tex]3x^2 - 2x - 16 = 3 \left(x^2 - \dfrac{2x}3\right) - 16 \\\\ ~~~~~~~~ = 3 \left(x^2 - \dfrac{2x}3 + \dfrac1{3^2}\right) - 16 - \dfrac13 \\\\ ~~~~~~~~ = 3 \left(x - \dfrac13\right)^2 - \dfrac{49}3[/tex]
Then
[tex]\dfrac{dy}{dx} = 3 \left(x - \dfrac13\right)^2 - \dfrac{49}3 \le 0 \\\\ ~~~~ \implies 3 \left(x - \dfrac13\right)^2 \le \dfrac{49}3 \\\\ ~~~~ \implies \left(x - \dfrac13\right)^2 \le \dfrac{49}9 \\\\ ~~~~ \implies \left|x - \dfrac13\right| \le \sqrt{\dfrac{49}9} = \dfrac73 \\\\ ~~~~ \implies x - \dfrac13 \le \dfrac73 \text{ or } -\left(x-\dfrac13\right) \le \dfrac73 \\\\ ~~~~ \implies \boxed{x \le 2 \text{ or } x \ge \dfrac83}[/tex]
Please help me solve the problem in the image. I found that a=-65 and b=17 and when I plug it in the equation it’s wrong
Answer:
-181 - 79x
Step-by-step explanation:
I am not sure your comment fits the given problem.
I get the following approach and solution :
T(1 + 4x) = 1×a + 4x×b = 2 + 2x
a = 2 + 2x - 4xb
T(4 + 15x) = 4×a + 15x×b = -3 + 3x
4×(2 + 2x - 4xb) + 15xb = -3 + 3x
8 + 8x - 16xb + 15xb = -3 + 3x
11 + 5x - xb = 0
11 + 5x = xb
b = (11 + 5x)/x
a = 2 + 2x - 4x(11 + 5x)/x = 2 + 2x - 44 - 20x = -42 - 18x
T(3 - 5x) = 3×a - 5xb = 3(-42 - 18x) - 5x(11 + 5x)/x =
= -126 - 54x - 55 - 25x = -181 - 79x
control :
T(1 + 4x) = a + 4xb = -42 - 18x + 44 + 20x = 2 + 2x
T(4 + 15x) = 4a + 15xb = -168 - 72x + 165 + 75x = -3 + 3x
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer:
-40x
Step-by-step explanation:
f(x) =-3x-5
g(x) =4x-2
(f+g)(x) =?
now,
f(g(x))
=f(4x-2)
=-3×4x-2-5
=-10×4x
=-40x
Find the variance of 24,30,17,22,22
Answer:
22
Step-by-step explanation:
Solve the right triangle.
b= 1.26 c=4.58
Need answers for A,B,a
I keep getting it wrong.
Answer:
a=4.40
Step-by-step explanation:
To find value of a use pythagoras theorem:
c^2=b^2+a^2
Rearrange the equation:
a^2=c^2-b^2
Substitute the values:
a^2=(4.58)^2-(1.26)^2
After calculation:
a=4.40
Given two independent random samples with the following results:
n1=13
x‾1=141
s1=13
n2=9
x‾2=161
s2=12
Use this data to find the 98% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 98% confidence interval. Round your answers to the nearest whole number.
please explain
The point estimate of difference of the sample his will be -20.
How to illustrate the information?Based on the information given, the. following can be depicted:
n1 = 13
x1 = 141
s1 = 13
n2 = 9
x2 = 161
s2 = 12
The point estimate of difference will be:
= 141 - 161
= -20
The margin of error to be used in constructing the confidence interval will be calculated by multiplying the standard error which is 5.467 and the critical value. This will be:
= 5.467 × 2.528
= 13.822
The margin of error is 13.822.
The confidence interval will now be:
= (-20 + 13.822) and (-20 - 13.822)
= -6.178 and -33.822
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George cuts a rectangular piece of glass down one of the diagonals as shown below. What is the length of the diagonal that he cut to the nearest whole inch? Enter only the number. An image shows a rectangle with length = 18 inches and width = 36 inches. A red dotted line crosses the rectangle from the upper left corner to the lower right corner.
The length of the diagonal that he cut to the nearest whole inch is 36 inches
TriangleA rectangle with length = 18 inchesWidth = 36 inchesA red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.
Length of the diagonal of a rectangle;
Hypotenuse² = adjacent² + opposite²
= 18² + 36²
= 324 + 1296
hyp² = 1620
Take the square root of both sideshyp = √1620
hyp = 35.4964786985976
Approximately,
hypotenuse = 36 inches
Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.
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Whole page of geometry stuff for 50 points only do 2,3 and 4 ( serious answers only or 1 star and report )
See below for the distance between the points and the lines
How to determine the distance between the lines and the points?Question 2
The line and the points are given as:
x = y
P = (4, -2)
Rewrite the equation as:
y = x
The slope of the above equation is
m = 1
The slope of a line perpendicular to it is
m = -1
A linear equation is represented as:
y = mx + b
Substitute m = -1
y = -x + b
Substitute (4, -2) in y = -x + b
-2 = -4 + b
Solve for b
b = 2
Substitute b = 2 in y = -x + b
y = -x + 2
So, we have:
x = y and y = -x + 2
Substitute x for y
x = -x + 2
Solve for x
x = 1
Substitute x = 1 in y = x
y = 1
So, we have the following points
(1, 1) and (4, -2)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(1 - 4)² + (1 + 2)²
Evaluate
d = 3√2
Hence, the distance between x = y and P = (4, -2) is 3√2 units
Question 3
The line and the points are given as:
y = 2x + 1
Q = (2, 10)
The slope of the above equation is
m = 2
The slope of a line perpendicular to it is
m = -1/2
A linear equation is represented as:
y = mx + b
Substitute m = -1/2
y = -1/2x + b
Substitute (2, 10) in y = -1/2x + b
10 = -1/2 * 2 + b
Solve for b
b = 11
Substitute b = 11 in y = -1/2x + b
y = -1/2x + 11
So, we have:
y = 2x + 1 and y = -1/2x + 11
Substitute 2x + 1 for y
2x + 1 = -1/2x + 11
Solve for x
x = 4
Substitute x = 4 in y = 2x + 1
y = 9
So, we have the following points
(4, 9) and (2, 10)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(4 - 2)² + (9 - 10)²
Evaluate
d = √5
Hence, the distance between the line and the point is √5 units
Question 4
The line and the points are given as:
y = -x + 3
R = (-5, 0)
The slope of the above equation is
m = -1
The slope of a line perpendicular to it is
m = 1
A linear equation is represented as:
y = mx + b
Substitute m = 1
y = x + b
Substitute (-5, 0) in y = x + b
0 = 5 + b
Solve for b
b = -5
Substitute b = 5 in y = x + b
y = x + 5
So, we have:
y = x + 5 and y = -x + 3
Substitute x + 5 for y
x + 5 = -x + 3
Solve for x
x = -1
Substitute x = -1 in y = x + 3
y = 2
So, we have the following points
(-1, 2) and (-5, 0)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(-1 + 5)² + (2 - 0)²
Evaluate
d = 2√5
Hence, the distance between the line and the point is 2√5 units
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Simplify the following expression:
( 4 + 5i ) / 4i
Select one:
a.
( 5 + 4i ) / 4
b.
( 5 - 4i ) / 4
c.
( 5i + 4i ) / 4
d.
( 5i - 4 ) / 4
Answer: B
Step-by-step explanation:
[tex]\frac{4+5i}{4i}\\ \\ =\frac{1}{4} \left(\frac{4+5i}{i} \right)\\\\=\frac{1}{4}((-i)(4+5i))\\\\=\frac{1}{4}(-4i-5i^2)\\\\=\frac{5-4i}{4}[/tex]
Consider the following descriptions of the platonic solids use them to complete the table
Answer:
4, 6, 4
6, 12, 8
8, 12, 6
Step-by-step explanation:
Tetrahedron:
4 faces, 6 edges, 4 vertices
Cube:
6 faces, 12 edges, 8 vertices
Octahedron:
8 faces, 12 edges, 6 vertices
you can also use the v - e + f = 2 to check
what the answers
help me'
Answer:
47°
Step-by-step explanation:
If angles are complementary, that means those angles are added up to 90°.
Therefore,
43 + x = 90
Take 43 to the right side to make x as the subject.
x = 90 - 43
x = 47°
Note that a complementary angle adds up to 90 degrees.
In this problem, we get the equation:
43° + x = 90°
So, we need to find the value of x by doing:
90° – 43° = 47°
x = 47°
43° + 47° = 90°
We get the final result as:
x = 47°
Hope this helps :)
A student purchased 7 binders for a total of $8.61. Write an equation that can be used to find the cost of each binder, n, in dollars.
The equation that can be used to find the cost of each binder n in dollars is 861=7n.
Given that the cost of 7 binders is $8.61.
We are required to form an equation that represents the total cost of each binder n in dollars.
Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.
Suppose the cost of 1 binder is n dollar.
We know that the total cost is basically the product of price of 1 unit and number of quantities of units.
Total cost=Price of 1 unit* number of units
8.61=n*7
8.61=7n
Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
Considering it's discriminant, it is found that:
A. The classmate is wrong, as the discriminant is of zero, hence the equation has one solution.
B. The quadratic equation has 1 x-intercept.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
y = ax^2 + bx + c
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.In this problem, the equation is:
y = 9x² - 6x + 1.
The coefficients are a = 9, b = -6 and c = 1, hence the discriminant is:
[tex]\Delta =(-6)^2 - 4(9)(1) = 36 - 36 = 0[/tex]
Since the discriminant is zero, the classmate is wrong, as it means that the equation has one solution = one x-intercept.
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If $6,000 principal plus $132.90 of simple interest was withdrawn on August 14, 2011, from an investment earning 5.5% interest, on what day was the money invested?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$132.90\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years \end{cases} \\\\\\ 132.90 = (6000)(0.055)(t)\implies \cfrac{132.90}{(6000)(0.055)}=t\implies \cfrac{443}{1100}=t \\\\\\ \stackrel{\textit{converting that to days}}{\cfrac{443}{1100}\cdot 365} ~~ \approx ~~ 147~days[/tex]
now, if we move back from August 14th by 147 days backwards, that'd put us on March 20th.
Let g be a one-to-one function and suppose f is the inverse function of g
if g(5)=11 and g(3)=5, find f(5)
Answer:
So g(6) comes out to be 2.
Step-by-step explanation:
So f(6)=5 means when f acts on 6, the result is 5....so the inverse would take 5 back to 6...or g(5)=6
So f(2)=6 means that f reassigns 2 to 6....so the inverse would take 6 back to 2....or g(6)=2
hope this helps :)
Answer: 3
Step-by-step explanation:
If f(x) = y, then invf(y) = x
So, f(5) = invg(5) = 3
HELP ME WITH THIS PLEASEEEE
Answer:
the perpendicular bisector
Explanation:
The perpendicular bisector will intersect the segment at its midpoint.
13. A data set has a mean of x=3905 and a standard deviation of 110. Find the z-score for each of the following.
14. A random sample of 80 tires showed that the mean mileage per tire was 41,400mi, with a standard deviation of 4700mi.
Question 13
Part (a)
[tex]\frac{3840-3905}{110}=\boxed{0.5\overline{90}}[/tex]
By similar logic, the other answers are
(b) 2.6818181....
(c) 3.5909090...
(d) 1.1363636...
Question 14
Part (a)
[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]
Part (b)
[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]
Review the graph of function j(x).
On a coordinate plane, a line starts at open circle (2, 6) and goes down through (negative 2, 2). A solid circle is at (3, 6). A curve goes from solid circle (2, 3) to open circle (3, 4). A line goes from the open circle to closed circle (6, 5).
What is Limit of j (x) as x approaches 3?
3
4
5
6
The limit of j (x) as x approaches 3 is 4.
According to the question, A line begins at an open circle (2, 6) on a coordinate plane and descends through ( -2, 2). At, a complete circle is (3, 6). From a solid circle (2, 3), a curve leads to an open circle (3, 4). From the open circle to the closed circle, a line runs (6, 5).
From the graph, it can be seen that the limit of the function j(x) as the value of x approaches 3 is 4.
A diagram or pictorial representation that organizes the depiction of data or values is known as a graph.
The relationships between two or more items are frequently represented by the points on a graph.
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Answer:
4
Step-by-step explanation:
egg 2023
Prove Sin(90-A)=cosA
Step-by-step explanation:
sin(90-A) = sin90cosA-sinAcos90
= cosA*1-0*sinA
= cos90
hence proved
Step-by-step explanation:
sin(90-A)=cosA
sin(90-A)=sin(90-A)
90-A=90-A
-A+A=90-90
=0
Need help with this!!
Answer:
below
Step-by-step explanation:
1) slope = rise / run
2 coordinates are (-4, 0), (0, 2).
2 - 0 = 2
0 -- 4 = 4
2 / 4 = 1/2 so the slope is 0.5 or ½
2) it crosses the y axis at the average of the origin and 4.
4 + 0 = 4 / 2 = 2 so y intercept is 2.
3) in y= mx + b form
f(x) = ½x + 2, or, f(x) = 0.5x + 2
A polynomial f (x) has the
given zeros of 6, -1, and -3.
Part A: Using the
Factor Theorem, determine the
polynomial f (x) in expanded form. Show all necessary
calculations.
*
Part B: Divide the polynomial f (x) by (x2 - x - 2) to
create a rational function g(x) in simplest factored form.
Determine g(x) and find its slant asymptote.
Part C: List all locations and types of discontinuities of
the function g(x).
a) The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.
b) The rational function g(x) in factored form is g(x) = [(x - 6) · (x + 3)] / (x - 2). there is no slant asymptotes.
c) There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.
How to analyze polynomial and rational functions
a) In the first part of this question we need to determine the equation of a polynomial in expanded form, derived from its factor form defined below:
f(x) = Π (x - rₐ), for a ∈ {1, 2, 3, 4, ..., n} (1)
Where rₐ is the a-th root of the polynomial.
If we know that r₁ = 6, r₂ = - 1 and r₃ = - 3, then the polynomial in factor form is:
f(x) = (x - 6) · (x + 1) · (x + 3)
f(x) = (x - 6) · (x² + 4 · x + 4)
f(x) = (x - 6) · x² + (x - 6) · (4 · x) + (x - 6) · 4
f(x) = x³ - 6 · x² + 4 · x² - 24 · x + 4 · x - 24
f(x) = x³ + 10 · x² - 20 · x - 24
The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.
b) The rational function is introduced below:
g(x) = (x³ + 10 · x² - 20 · x - 24) / (x² - x - 2)
g(x) = [(x - 6) · (x + 1) · (x + 3)] / [(x - 2) · (x + 1)]
g(x) = [(x - 6) · (x + 3)] / (x - 2)
The slope of the slant asymptote is:
m = lim [g(x) / x] for x → ± ∞
m = [(x - 6) · (x + 3)] / [x · (x - 2)]
m = 1
And the intercept of the slant asymptote is:
n = lim [g(x) - m · x] for x → ± ∞
n = Non-existent
Hence, there is no slant asymptotes.
c) There is vertical asymptote at a x-point if the denominator is equal to zero. There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.
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What is the smallest odd number of using 9,3,6,8,1,9
Answer: well one is
Bc its the smallest besides zero, but zero is neither odd or even
Step-by-step explanation:
A lateral thoracic spine on a 33-cm patient is usually taken using 100 mA (large focal spot), 0.5 seconds, 86 kVp, 40-inch SID, 12:1 grid ratio. If the mA is increased to 400 to stop motion blur from tremors, which of the following technique changes will produce a radiographic density and contrast most similar to the original?
A 0.13 sec and a 86 kVp technical changes are the changes that would have to produce the radiographic density and the contrast that are more similar to the original.
What is the radiographic density?The radio graphic density can de defined to be the total amount or the overall darkening that can be found in a particular radiograph. This is usually known to have a certain type of density range that lies between 0.3 to 2.0 density.
When there is a density that is less than 0.3, the problem is basically because there is the issue of the density which would be found at the base and the fact that the film that is being used has fog in it.
It is known that based on the values that we have here the density and contrast would have to be of the given kvp of 86 and 0.13 seconds in order to be said to be similar to the original.
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