Answer:
$13,082.60 more
Step-by-step explanation:
Melanie:
[tex]A=P(1+\frac{r}{n})^(20)\\ A=9800(1+\frac{.045}{4})^(20)\\A=$12,257.36[/tex]
Amelia:
[tex]A=Pe^(rt)\\A=9800e^(.0475*20)\\A=$25,339.95[/tex]
Amelia-Melanie= $13,082.60
Which transformations are needed to change the parent cosine function to y = 0. 35 cosine (8 (x minus StartFraction pi Over 4 EndFraction))? vertical stretch of 0. 35, horizontal stretch to a period of 16 pi, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical compression of 0. 35, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 4 EndFraction units to the left vertical compression of 0. 35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical stretch of 0. 35, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right.
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
https://brainly.com/question/17006186
Draw a picture to answer.
what is 1/4 of 12?
Answer:
3
Step-by-step explanation:
1/4 x12= 12/4
12/4=3
PLEASE HURRY! (once more)
A cooler contains three colas, seven root beers, and three ginger ales. Three people grab a drink at random, one at a time.
a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs a cola?
b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
Answer:
a) 3/286
b) 7/286
Step-by-step explanation:
We start with 13 drinks. After the first person takes one drink, there are 12 drinks left, After the second person takes one drink, there are 11 drinks available for the third person.
a) From the 13 drinks, there are 3 colas, From the 12 remaining drinks, there are 3 ginger ales. From the 11 remaining drinks, there are 2 colas. We have:
[tex] \frac{3}{13} \times \frac{3}{12} \times \frac{2}{11} = \frac{3}{286} [/tex]
b) From the 13 drinks, there are 3 colas. From the 12 remaining drinks, there are 2 colas. From the 11 remaining drinks, there are 7 root beers. We have:
[tex] \frac{3}{13} \times \frac{2}{12} \times \frac{7}{11} = \frac{7}{286} [/tex]
Which geometric figure would be the best to model a suitcase?
Answer:
A rectangular prism would be best to model a suitcase
Step-by-step explanation:
Hope that helps!
Answer:
Rectangular Prism
Step-by-step explanation:
If you look at a suitcase, it resembles a rectangular prism quite well.
Quick!!! Solve for the missing lengths using trigonometric ratios.
*
110m
42°
Х
Answer:
see explanation
Step-by-step explanation:
using the tangent ratio in the right triangle to find x
tan42° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{10}{x}[/tex] ( multiply both sides by x )
x × tan42° = 10 ( divide both sides by tan42° )
x = [tex]\frac{10}{tan42}[/tex] ≈ 11.1 ( to 1 dec. place )
-------------------------------------------------
using the sine ratio to find the hypotenuse h
sin42° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{h}[/tex] ( multiply both sides by h )
h × sin42° = 10 ( divide both sides by sin42° )
h = [tex]\frac{10}{sin42}[/tex] ≈ 14.9 ( to 1 dec. place )
A plane flies 100km north and then flies 400km south, what is its new position?
Answer:
300km south
Step-by-step explanation:
Go up once from original position then down four times
determine if the relationships are linear and if so are they proportional
jeff is 1.67 meters tall how many centimeters tall is jeff
Answer:
167
Step-by-step explanation:
Round to the ten millions place.
3,025,285,000
o a. 3,025,290,000
o b. 3,020,000,000
c. 3,025,000,000
d. 3,030,000,000
o e. 3,030,285,000
Best answer gets brainliest
Answer:
The answer is 30.
Step-by-step explanation:
12+12+6= 30
I got 6 because it shows a semi circle, and half of 12 is 6.
Answer:
30
Step-by-step explanation:
one circle = 12
two circle = 12 × 2 = 24
half circle = 12/2 = 6
so
two circle + half circle = 24 + 6 = 30
Ms. Lee takes out a loan to start a business. She borrows $5,000 of a simple annual interest rate of 6. 5% for 5 years. What is the total amount of interest Ms Lee must pay
Answer:
A = $6,625.00
Step-by-step explanation:
A = P(1 + rt)
A = 5000(1 + (0.065 × 5)) = 6625
helppp plsss. i have to turn this in asap
Answer:
y= 2x-5
Step-by-step explanation:
The slope formula is m=(y2-y1)/(x2-x1)
-3-1 / 1-3 = -4/-2= 2=m
The Y interception- y=mx+b using coordinates (3,1)
1=2(3)+b
1=6+b (subtracting 6 on both sides to isolate b)
-5=b
plug it in
y=2x-5
if there are 15 plane 2 crash 1 breakdown how many planes are left
Answer:
15 planes
Step-by-step explanation:
none disappear, just change shape/ability. its a riddle.
Answer:
15-2-1 = 15-3 = 12.
there are 12 planes left.
Step-by-step explanation:
hope this helped have a nice day
Solve the equation for x:
3x+5=20
Answer:
x = 5
Step-by-step explanation:
3x+5=20
Subtract 5 from both sides.
3x=20−5
Subtract 5 from 20 to get 15.
3x=15
Divide both sides by 3.
x= 15/3
Divide 15 by 3 to get 5.
x=5
What is 3/7 as a decimal rounded to 3 decimal places?
Please help! Will mark brainliest <3. (Click on the photo too see the question!) you need to select all angle pairs that are vertical angles.
Answer:
B and D
Step-by-step explanation:
vertical angles are ones that are formed by intersecting lines, and they are also equal to each other and opposite of each other.
its not A because they are not equal to each other.
B is correct because they are formed by intersecting line and equal to each other
C is incorrect since theres some random line that doesnt completely pass through on either side
D is correct
Help pleaseee i am awful at math
Step-by-step explanation:
use the above process and answer is $3.60
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answer:
(3,5)
Step-by-step explanation:
We first need to substitute x for 3 in the equation :)
y = 2(3) - 1
y = 6 - 1
y = 5
The cordinate will be (3,5)
Have an amazing day!!
Please rate and mark brainliest!!
Element X decays radioactively with a half life of 7 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?
Answer:
32.3m
Step-by-step explanation:
Use equation A = Ao(0.5)^(t/t½)
Now input values: 40 = 980(0.5)^(t/7)
rearrange for t: t = [7ln(2/49)]/ / ln(0.5). Then from here, you can extract 32.3 as your answer
Answer:
t = 32.3 min
Step-by-step explanation:
This is an example of half-life exponential decay.
For situations like this we have a formula.
[tex]N = N_{0} * (\frac{1}{2})^n[/tex]
N represents the end amount of parent element, N (naught) represents the starting amount of the parent element, and n being the amount half-lifes that have occurred.
Now n, can be broken down further into t/p, which means the time elapsed (t) divided by time it takes for one decay period (p), which essentially gives you the amount of half-lifes that have occurred. So you can represent the formula as:
[tex]N = N_{0} * (\frac{1}{2})^{t/p}[/tex]
The question tells you you start off with 980 grams of Element x, so put that for N naught. [tex]N = 980g * (\frac{1}{2})^{t/p}[/tex]. Then it tells you half-life is 7 minutes, which means the period it takes for one half-life to occur is 7, which is p. [tex]N = 980g * (\frac{1}{2})^{t/7min}[/tex]. You are also told that you end up with 40 grams, so put that in for N. [tex]40g = 980g * (\frac{1}{2})^{t/7min}[/tex]. Now we solve for t, the time elapsed.
(This is the part where you use logs to solve, but if you are still rough on this, I'll walk you through it)
Start off by dividing on both sides.
[tex]\frac{40g}{980g} = (\frac{1}{2})^{t/7min} \\, \frac{2}{49} = (\frac{1}{2})^{t/7min}[/tex]
Take the log of both sides.
[tex]log(\frac{2}{49}) = log( (\frac{1}{2})^{t/7min})[/tex]
Now we gotta get t out of the exponent, we'll do this by using log laws. More specifically the exponent law for log laws which states. [tex]log(b^x) = x*log(b)[/tex]. If we apply that to our situation like so.. [tex]log((\frac{1}{2})^{t/7min}) = \frac{t}{7min} * log(\frac{1}{2})[/tex]
Now our whole equation now looks like this:
[tex]log(\frac{2}{49}) = \frac{t}{7min} * log( \frac{1}{2})[/tex]
keep simplifying,
[tex]\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = \frac{t}{7min}[/tex]
[tex]7min *\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = t\\\\t = 32.3min \\[/tex]
Now you have your answer!
If we want to know if diagonals or sides are congruent we would use the
formula.
distance
midpoint
slope
When we want to know if the diagonals or sides are congruent we would use the D. Slope.
What is congruent?It should be noted that congruent in geometry simply means when two objects have same shapes and size.
In this case, when we want to know if the diagonals or sides are congruent we would use the slope. This can show the equality in the shape.
Learn more about congruent on:
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An isosceles triangle has an angle that measures 38degrees. What measures are possible for the other two angles? Choose all that apply.
Answer:
71° and 71°.⠀
Step-by-step explanation:
The triangle having two sides equal along with one different side is called an isosceles triangle.
⠀
So, Let us assume the other sides (two equal sides) of the isosceles triangle as x. As the different side is already given in the question.⠀
We know that,
The sum of all angles of a triangle is 180°⠀
So, According to the question :
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]
⠀
[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]
⠀
Therefore,
The measure of the two other angles of the isosceles triangle are 71° and 71°.The table shows the sales receipt for your purchase.
a) the items with a "t" next to the price are subject to sales tax. what percent sales tax did you pay?
b) calculate the price of the top.
c) the price you paid for the top was 60% of the original price. what was the original price of the top?
The sales receipt for the purchase includes the sales tax
The sales tax is 6%The price at the top is $7.50The original price at the top is $12.50How to determine the percent of sales tax?The sales tax is calculated as:
Percentage sales tax * (Sum of Items subjected to tax) = Sales tax.
So, we have:
T * (3 + 0.5) = 0.21
Evaluate the sum
T * (3.5) = 0.21
Divide both sides by 3.5
T = 6%
Hence, the sales tax is 6%
The price at the topThe price (p) at the top is calculated using:
p = 13 - 3 - 2 - 0.5
Evaluate the difference
p = 7.5
Hence, the price at the top is $7.50
The original price at the top60% of the original price (P) is p.
So, we have:
60% * P = p
Substitute 7.5 for p
60% * P = 7.5
Divide both sides by 60%
P = 12.5
Hence, the original price at the top is $12.50
Read more about sales tax and discounts at:
https://brainly.com/question/11648148
-2x + 1 = 4x + 9
I don’t know what to solve for x?
Answer:
x = -1.33333333333
Step-by-step explanation:
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x+1-1=4x+9-1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-2x=4x+8[/tex]
[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}[/tex]
[tex]-2x-4x=4x+8-4x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-6x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]
[tex]\frac{-6x}{-6}=\frac{8}{-6}[/tex]
[tex]x=-\frac{4}{3}[/tex]
[tex]x=-1.33333333333[/tex]
~Lenvy~
A polynomial p(x) has 3, 2-i, and √3 as its roots and goes through (0,-90), find p(x)
Answer:
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Step-by-step explanation:
Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...
{3, 2 -i, 2 +i, √3, -√3}
Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.
__
Factored formThen the factored p(x) will be ...
p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k
Simplifying a bit, we have ...
p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)
__
Scale factorAt x=0, this evaluates to ...
p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k
We want p(0) = -90, so we require ...
45k = -90
k = -2
__
Then the function p(x) factored to integers is ...
p(x) = -2(x -3)(x² -4x +5)(x² -3)
When we multiply this out, we find the standard form equation is ...
p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90
Solve the System of equations x = -2 ; y = 3 .(Choose from a,b, or c. Show your work step by step).
a) x+y=1
2x+y=5
b) x+2y = 4
x +y = 1
c) x-y=-5
x+y= 11
Pls show your work as I want to understand how to solve this type of equation.
Answer:
B is a the answers for the question
please mark me as brainlest
please no guessing (WILL GIVE BRAINILIST)
STATISTICS
Answer:
#2 mean is 90.3846154 and range is 40
#3 mean 91.9230769 and range is 20
(you might have mixed the second and third graph up)
Step-by-step explanation:
2. You are building a fence around your vegetable garden in your backyard. If
the garden is 12'8" long and 4'6" wide, what is the total length of fencing you
will need?
The length of fencing required is 34.34 feet.
Data;
Length = 12 feet 8 inch long = (12 + 0.67) feet = 12.67 feetWidth = 4 feet 6 inch wide = (4+0.5)feet = 4.5 feetPerimeter of the GardenTo find the total length of fencing required, we have to find the perimeter of a rectangle since the garden has a rectangular shape.
[tex]P = 2(L + W)[/tex]
We can substitute the values in the formula of perimeter above and proceed to solve.
[tex]P = 2(L+W) \\P = 2(12.67 + 4.5) \\P = 2(17.17)\\P = 34.34ft[/tex]
The length of fencing required is 34.34 feet.
Learn more on perimeter of a rectangle here;
https://brainly.com/question/12274271
The bearing of a point K from a point L is 084 degrees. What is the bearing of L from K
Answer:
if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree
The bearing of a point L from a point K is 264 degrees.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
The bearing of a point K from a point L is 084 degrees.
Now,
Since, The bearing of a point K from a point L is 084 degrees.
Hence, The bearing of a point L from a point K = 180° + 84°
= 264°
Thus, The bearing of a point L from a point K is 264 degrees.
Learn more about the addition visit:
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#SPJ2
Photo attached with instructions
Step-by-step explanation:
using cosine rule,
BC²= AC² + BC² - 2*AC*BC*COSc
= 13² + 6² - 2*13*6*-cos(180-91)
= 169 + 36 - (-2.72)
= 202.28
√BC² = √202.28
BC = 14.22
BC = 14.20cm to nearest tenth
For a lab experiment, Jeremy needs to know the volume of a sample of tin with a mass of 189.8 grams.
Use the chart to find the volume of this sample of tin.
Answer:
26 cm^3
Step-by-step explanation:
189.8 gm / ( 7.3 gm / cm^3) = 26 cm^3
Answer:
C) 26cm
Step-by-step explanation:
hope it helps!