Answer:
0.50 or about half a year longer.
Step-by-step explanation:
We can write an equation to model bot investments.
Oliver invested $970 in an account paying an interest rate of 7.5% compounded continuously.
Recall that continuous compound is given by the equation:
[tex]A = Pe^{rt}[/tex]
Where A is the amount afterwards, P is the principal amount, r is the rate, and t is the time in years.
Since the initial investment is $970 at a rate of 7.5%:
[tex]A = 970e^{0.075t}[/tex]
Carson invested $970 in an account paying an interest rate of 7.375% compounded annually.
Recall that compound interest is given by the equation:
[tex]\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}[/tex]
Where A is the amount afterwards, P is the principal amount, r is the rate, n is the number of times compounded per year, and t is the time in years.
Since the initial investment is $970 at a rate of 7.375% compounded annually:
[tex]\displaystyle A = 970\left(1+\frac{0.07375}{1}\right)^{(1)t}=970(1.07375)^t[/tex]
When Oliver's money doubles, he will have $1,940 afterwards. Hence:
[tex]1940= 970e^{0.075t}[/tex]
Solve for t:
[tex]\displaystyle 2 = e^{0.075t}[/tex]
Take the natural log of both sides:
[tex]\ln\left (2\right) = \ln\left(e^{0.075t}\right)[/tex]
Simplify:
[tex]\ln(2) = 0.075t\Rightarrow \displaystyle t = \frac{\ln(2)}{0.075}\text{ years}[/tex]
When Carson's money doubles, he will have $1,940 afterwards. Hence:
[tex]\displaystyle 1940=970(1.07375)^t[/tex]
Solve for t:
[tex]2=(1.07375)^t[/tex]
Take the natural log of both sides:
[tex]\ln(2)=\ln\left((1.07375)^t\right)[/tex]
Simplify:
[tex]\ln(2)=t\ln\left((1.07375)\right)[/tex]
Hence:
[tex]\displaystyle t = \frac{\ln(2)}{\ln(1.07375)}[/tex]
Then it will take Carson's money:
[tex]\displaystyle \Delta t = \frac{\ln(2)}{\ln(1.07375)}-\frac{\ln(2)}{0.075}=0.4991\approx 0.50[/tex]
About 0.50 or half a year longer to double than Oliver's money.
Which statements are correct? Check all that apply.
Answer:
e s r
Step-by-step explanation:
36. Factorize x-12x + 20
Solve for x. round to the nearest tenth, if necessary.
Answer:
29
Step-by-step explanation:
all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151
then 180-151=29
SEE QUESTION IN IMAGE
Answer:
Step-by-step explanation:
[tex]Mean=\frac{all.ages.added.together.of.all.kids}{total.number.of.kids}[/tex] Hopefully, that makes sense! To get the numerator of that problem, we take the number of kids and multiply it by the corresponding age and add them all together. To get the denominator, we add the total number of kids together. That will look like this mathematically, setting the mean equal to 14.44, as stated:
[tex]14.44=\frac{13(15)+14(42)+15X+16(10)+17(3)}{15+42+X+10+3}[/tex] and simplify that a bit to
[tex]14.44=\frac{195+588+15X+160+51}{70+X}[/tex] and a bit more to
[tex]14.44=\frac{994+15X}{70+X}[/tex] and cross multiply
14.44(70 + X) = 994 + 15X and
1010.8 + 14.44X = 994 + 15X and
16.8 = .56X so
X = 30
30 kids are 15 years old for the mean age to be 14.44
d.30
Answer:
Solution given:
x. [tex] \:\:\:[/tex] f. [tex] \:\:\:[/tex] fx
13. [tex] \:\:\:[/tex] 15. [tex] \:\:\:[/tex] 195
14.[tex] \:\:\:[/tex] 42 [tex] \:\:\:[/tex] 588
15. [tex] \:\:\:[/tex] x. [tex] \:\:\:[/tex] 15x
16. [tex] \:\:\:[/tex] 10. [tex] \:\:\:[/tex] 160
17. [tex] \:\:\:[/tex] 3. [tex] \:\:\:[/tex] 51
. n=70+x. [tex]\sum[/tex]=994+15x
we have
mean=sum/n
14.44=[tex]\bold{\frac{\sum}{n}}[/tex]
14.44=[tex]\bold{\frac{994+15x}{70+x}}[/tex]
doing crisscrossed multiplication
(70+x)*14.44=994+15x
1010.8+14.44x=994+15x
15x-14.44x=1010.8-994
0.56x=16.8
x=16.8/0.56
x=30
I need help with this math problem
GP
We have
(a + bx) / (a - bx) = (b + cx) / (b - cx)
==> (a + bx) (b - cx) = (a - bx) (b + cx)
==> ab + (b ² - ac) x - bcx ² = ab + (ac - b ²) x - bcx ²
==> (b ² - ac) x = (ac - b ²) x
==> b ² - ac = ac - b ²
==> 2b ² = 2ac
==> b ² = ac … … … [1]
Similarly, you would find
(a + bx) / (a - bx) = (c + dx) / (c - dx)
==> ad = bc … … … [2]
and
(b + cx) / (b - cx) = (c + dx) / (c - dx)
==> c ² = bd … … … [3]
Now:
c ² = bd ==> b = c ² / d
b ² = ac ==> c = b ² / a
ad = bc ==> d = bc / a
and we find
d / c = (bc / a) / (b ² / a) = c / b
and
c / b = (b ² / a) / (c ² / d) = (b ² d) / (a c ²) = b / a
which is to say, the ratio between d and c is equal to the ratio between c and b, and also equal to the ratio between b and a. Therefore (a, b, c, d) are in a geometric progression.
HHHHELP ME!!!!!! PLZ
Total gasoline = 10 gallons
Gasoline left after 100 miles = 5 gallons
Gasoline used in 100 miles
= Total gasoline - Gasoline left after 100 miles
= 10 gallons - 5 gallons
= 5 gallons
Gasoline used in 1 mile
= Gasoline used in 100 miles/100
= 5 gallons/100
= 0.05 gallons
4.Find the first five terms of the recursive sequence
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Parallelogram PARL is similar to parallelogram WXYZ. If AP = 7, PL = 15, and WZ = 45, find the value of c.
Answer:
c = 21
Step-by-step explanation:
**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**
If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.
PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.
With that in mind, we can apply this ratio to find WX.
We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.
c = 21
Hope this helps (●'◡'●)
-2/3a+5/6a-1/5a-1/6
Answer:
[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]
Step-by-step explanation:
classify the following as a chemical or physical: hydrogen gas is very explosive
Answer:
chemical
Step-by-step explanation:
What is the solution to this equation?
log_8 16 + 2log_8x =2
The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
Given the equation
[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2
We know that,
xlogb = log[tex]b^{x}[/tex]
So,
2[tex]log_{8}[/tex](x) = logx²
For the same base
logA + logB = log(AB)
So,
[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2
[tex]log_{8}[/tex](16x²) = 2
We know that
[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]
so,
[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²
x = 2 hence x = 2 will be correct answer.
For more about logarithm
https://brainly.com/question/20785664
#SPJ2
If a = 1/2, then a^2=
(A) -1
(B) 4
(C) 0
(D) 1
Answer:
1/4
Step-by-step explanation:
a^2
Let a= 1/2
(1/2)^2
(1/4)
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Multiply. (Use photo). Enter your answer in simplest radical form.
Answer:
72√2
Step-by-step explanation:
3√2 × 2√8 × √3 × √6
The above can be simplified as follow:
3√2 × 2√8 × √3 × √6
Recall
a√c × b√d = (a×b)√(c×d)
3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)
= 6√288
Recall
288 = 144 × 2
6√288 = 6√(144 × 2)
Recall
√(a×b) = √a × √b
6√(144 × 2) = 6 × √144 × √2
= 6 × 12 × √2
= 72√2
Therefore,
3√2 × 2√8 × √3 × √6 = 72√2
Be sure to show your work and solve for e:
17 + e + 11 = 56
What is the slope of the line that contains the points in the table?
х
У
15
-2
9
ON
3
4
-3
O A. 3
O B. -6
O c. 2
O D. -3
Answer:
https://www.dasd.org › 4444PDF
Web results
Entering Algebra 2: Answer Key
HEELLLPPPPPP what’s the answer????????????????????????? HEELLLLLLLPPPPPPPPPPPPPP
Answer:
(-2,-2)
Step-by-step explanation:
x^2 + y^2 = 9
A circle has an equation of the form
(x-h)^2 + (y-k)^2 = r^2
where the center is at ( h,k) and the radius is r
The circle is centered at (0,0) and has a radius 3
The only point entirely within the circle must have points less than 3
(-2,-2)
How do I solve this math equation: 7=8-p
Answer:
p = 1
Step-by-step explanation:
7 = 8 - p
7 + p = 8
p = 8-7
p = 1
Answered by Gauthmath
Can someone help me in this plz
Answer:
a =2 5
b =50
Step-by-step explanation:
Help, please, I'll give brainliest
Find the slope between (-2,-2) and (0,-3)
Answer:
Step-by-step explanation:
x1 y1 x2 y2
-2 -2 0 3
ΔY 5
ΔX 2
slope= 2 1/2
B= 3
Y =2.5X +3
Fill in the following statements.
DE ||
2DE =
Answer:
DE ║ BC
BC = 2(DE)
Step-by-step explanation:
From the picture attached,
AD = DB [Given]
AE = EC [Given]
Therefore, points D and E will be the midpoints of the sides AB and AC.
By midsegment theorem,
Segment joining midpoints of the two sides of a triangle is parallel and measures the half of the third side of the triangle.
DE ║ BC
DE = [tex]\frac{1}{2}(BC)[/tex]
BC = 2(DE)
ZEFG and ZGFH are a linear pair, mZEFG = 2n + 16, and mZGFH = 3n+24. What are mZEFG and mZGFH?
mZEFG =
Answer:
m<EFG = 72°
m<GFH = 108°
Step-by-step explanation:
m<EFG = 2n + 16
m<GFH = 3n + 24
Linear pairs are supplementary, therefore,
m<EFG + m<GFH = 180°
Substitute
2n + 16 + 3n + 24 = 180
Add like terms
5n + 40 = 180
5n + 40 - 40 = 180 - 40 (subtraction property of equality)
5n = 140
5n/5 = 140/5 (division property of equality)
n = 28
✔️m<EFG = 2n + 16
Plug in the value of n
m<EFG = 2(28) + 16 = 72°
✔️m<GFH = 3n + 24
Plug in the value of n
m<GFH = 3(28) + 24 = 108°
The value of 9.6 x 10000 lies between
a) 800 and 900
b)300 and 400
c) 80 and 90
d) 30 and 40
Answer:
option A is write answer
I hope you help
Answer:
none of these
Step-by-step explanation:
it's 96000 so none
Solve the equation sine Ф=0.6792 for 0°≤Ф≤360
Answer:
42.78⁹, 137.22⁹.
Step-by-step explanation:
sine Ф=0.6792
Angle Ф in the first quadrant = 42.78 degrees.
The sine is also positive in the second quadrant so the second solutio is
180 - 42.78
= 137.33 degres.
Hi I need help with this question please!!! I don’t understand it :/
Answer:
- 22.5
Step-by-step explanation:
Substitute x = 3 into f(x) and x = 16 into h(x) , then
[tex]\frac{1}{2}[/tex] g(3) - h(16)
= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)
= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)
= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)
= - 13.5 - 9
= - 22.5
Please I need some help!
Answer:
A
Step-by-step explanation:
A compressed by a factor of 1/4 in the y or vertical direction
find the measure of acute angle of a right angle triangle when one angle is 60°
Answer:
30 degrees.
Step-by-step explanation:
Let the acute angle be x.
Then as the 2 acute angles in a right triangle sum to 90 degrees,
x = 90 - 60
= 30.
We used the information we know to give us this equation.
90°+60°+x=180°
We add 90° and 60° to give 150°
150°+x=180°
x must therefore be 30°Bagels cost 35p each how much is 6?
Answer:
1 = 35p
6 = 35p×6
= 240p
Therefore, 6 bagels cost 240 p
Can someone Answer this
Answer:
tan x = c/b
cos x = b/a
sin x = c/a
Step-by-step explanation:
an easy way to memorize it would be SOH CAH TOA
SOH = sin, opposite, hypotunese
-- you find the angle and you divide it's opposite and hypotunese when it asks for sin
CAH = cos, adjacent, hypotunese
-- you find the angle's adjacent side and hypotunese, then divide
TOA = tan, opposite, adjacent
-- you find the angle's opposite side and divide it by the adjacent side
Given a right triangle with an acute angle Θ , if sin Θ = cos Θ , describe what this triangle would look like.
For sinø = cosø, ø = 45°. Because it is right, it is also a right, isosceles triangle
