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salantis [7]
2 years ago
9

Robbie owns 15 % more movies than Rebecca, and Rebecca owns 10 % more movies than Joshua. If Rebecca owns 220 movies, how many m

ovies do Robbie and Joshua each have?
Mathematics
1 answer:
sammy [17]2 years ago
4 0

Step-by-step explanation:

Robbie=

15%/100%=220

=33 movies

Rebecca=

10%/100%=220

11 movies

Robbie have 33 movies and Joshua have 11 movies

Thank you

Hope it helps.

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PLZZ HELLLPPPPPPPPPPPPPPPPPp
Licemer1 [7]

Answer:

please send the question thnx

Step-by-step explanation:

6 0
3 years ago
Use the Integral Test to determine whether the series is convergent or divergent
Inga [223]

Answer:

A. \sum_{n=1}^{\infty}\frac{n}{e^{15n}} converges by integral test

Step-by-step explanation:

A. At first we need to verify that the function which the series is related (\frac{n}{e^{15n}}) fills the necessary conditions to ensure that the test is effective.

*f(x) must be continuous or differentiable

*f(x) must be positive and decreasing

Let´s verify that f(x)=\frac{n}{e^{15n}} fills these conditions:

*Considering that eˣ≠0 for all x, the function f(x)=\frac{n}{e^{15n}} does not have any discontinuities, so it´s continuous

*Because eˣ is increasing:

      if a<b ,then eᵃ<eᵇ

      if 0<eᵃ<eᵇ ,then 1/eᵃ > 1/eᵇ

      if 1/eᵃ > 1/eᵇ and a<b, then a/eᵃ<b/eᵇ

  We conclude that f(x)=\frac{n}{e^{15n}} is decreasing

*Because eˣ is always positive and the sum is going from 1 to ∞, this show that f(x)=\frac{n}{e^{15n}} is positive in [1,∞).

Now we are able to use the integral test in f(x)=\frac{n}{e^{15n}} as follows:

\sum_{n=1}^{\infty}\frac{n}{e^{15n}}\ converges\ \leftrightarrow\ \int_{1}^{\infty}\frac{x}{e^{15x}}\ dx\ converges

Let´s proceed to integrate f(x) using integration by parts

\int_{1}^{\infty}\frac{x}{e^{15x}}\ dx=\int_{1}^{\infty}xe^{-15x}\ dx

Choose your U and dV like this:

U=x\ \rightarrow dU=1\\ dV=e^{-15x}\ \rightarrow V=\frac{-e^{-15x}}{15}

And continue using the formula for integration by parts:

\int_{1}^{\infty}Udv = UV|_{1}^{\infty} - \int_{1}^{\infty}Vdu

\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15} \int_{1}^{\infty}e^{-15x}\ dx

\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{-1}{15}(\frac{-1}{15e^{15x}})|_{1}^{\infty}

\int_{1}^{\infty}xe^{-15x}\ dx= \frac{-x}{15e^{15x}}|_{1}^{\infty} -\frac{1}{225e^{15x}}|_{1}^{\infty}

Because we are dealing with ∞, we´d rewrite it as a limit that will help us at the end of the integral:

\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}}(\frac{-x}{15e^{15x}}|_{1}^{b}-\frac{1}{225e^{15x}}|_{1}^{b})

\int_{1}^{\infty}xe^{-15x}\ dx= \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}}-(\frac{-1}{15e^{15}}-\frac{1}{225e^{15}})

\int_{1}^{\infty}xe^{-15x}\ dx= ( \lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}})+\frac{1}{15e^{15}}(1-\frac{1}{15})

We only have left to solve the limits, but because b goes to  ∞ and it is in an exponential function on the denominator everything goes to 0

\lim_{b \to{\infty}} \frac{-b}{15e^{15b}}-\frac{1}{225e^{15b}} = 0

\int_{1}^{\infty}xe^{-15x}\ dx= \frac{1}{15e^{15}}(1-\frac{1}{15})

Showing that the integral converges, it´s the same as showing that the series converges.

By the integral test \sum_{n=1}^{\infty}\frac{n}{e^{15n}} converges

7 0
2 years ago
What is the simplified answer and how to find it
stiv31 [10]
There you go:), hope was helpful

7 0
3 years ago
In ΔJKL, l = 860 inches, j = 920 inches and ∠K=126°. Find ∠L, to the nearest degree.
fomenos

Answer:

26

Step-by-step explanation:

JKL= ABC,  jkl=abc

1.) use law of sines to find k.

c^{2} =a^{2} +b^{2} -2abCosC    

c=\sqrt{920^{2} +860^{2} -2(920)(860)cos(126) } = 1586.225515

2.) use law of cosines to find L

\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}  

plug in for b and c:  \frac{860}{sinB} =\frac{1586.225515}{sin126}

cross multiply: \frac{1586.23sinB}{1586.23} =\frac{860sin126}{1586.23}

sinB= 0.4386227612\\B=sin^-1(0.4386227612)= 26.01604086\\

L=26

5 0
3 years ago
*PLEASE HELP WILL GIVE 60 POINTS I'M DESPERATE*
Zina [86]

Answer:

(0, 3)

Step-by-step explanation:

1. Find the slope:

\frac{y_{2} -y_{1} }{x_{2}-x_{1}  } =\frac{0-(-3)}{-4-(-8)}\\ \\=\frac{3}{4}

2. Calculate the y-intercept using a given point:

(-8, -3)

-3 = \frac{3}{4} (-8) + b

-3 = -6 + b

-3+6 = -6+6 + b

3 = b

3. Write in slope intercept form:

y= \frac{3}{4} x+3

Therefore, the y-intercept is 3.

The graph for this table is shown below.

hope this helps :)

4 0
2 years ago
Read 2 more answers
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