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Xelga [282]
3 years ago
12

Jacob makes the following statement: "I have a 60% chance of being selected as the captain of the baseball team and a 20% chance

of being elected student body president." What is the probability that Jacob will be selected as the captain of the baseball team and will be elected student body president? 80% 40% 12% 8%
Mathematics
1 answer:
Tanzania [10]3 years ago
6 0
It is 40% chance because subtract the baseball captain and the the body president
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From his home, Logan would have to walk due north to get to his friend Estelle's house and
Finger [1]

9514 1404 393

Answer:

  3.3 miles

Step-by-step explanation:

The distance can be found using the Pythagorean theorem.

  LV² +LE² = VE²

  LE² = VE² -LV² = 6² -5² = 36 -25 = 11

  LE = √11 ≈ 3.3

It is about 3.3 miles from Logan's house to Estelle's house.

5 0
3 years ago
Integration questions .
dlinn [17]
<h2>1)</h2>

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\textbf{b)}\\\\~~~~\displaystyle \int(3e^{-2x} +\cos (0.5 x)) dx\\\\=3\displaystyle \int e^{-2x} ~dx+ \displaystyle \int \cos(0.5 x) ~dx\\\\\\=-\dfrac 32 e^{-2x} + \dfrac 1{0.5} \sin (0.5 x) +C~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx}~dx = \dfrac 1m e^{mx} +C \right]\\\\\\=-\dfrac 32 e^{-2x} + 2 \sin(0.5 x) +C~~~~~~~~~~~~~~~~~;\left[\displaystyle \int \cos(mx)~ dx  = \dfrac 1m \sin(mx) +C\right]\\\\\\=-1.5e^{-2x} +2\sin(0.5x) +C

<h2>2)</h2>

\textbf{a)}\\\\y = \displaystyle \int \cos(x+5) ~ dx\\\\\text{Let,}\\\\~~~~~~~u = x+5\\\\\implies \dfrac{du}{dx} = 1+0~~~~~~;[\text{Differentiate both sides.}]\\\\\implies \dfrac{du}{dx} = 1\\\\\implies du = dx\\\\\text{Now,}\\\\y= \displaystyle \int \cos u ~ du\\\\~~~= \sin u +C\\\\~~~=\sin(x+5) + C

\textbf{b)}\\\\y = \displaystyle \int 2(5x-3)^4 dx\\\\\text{Let,}\\~~~~~~~~u = 5x-3\\\\\implies \dfrac{du}{dx} = 5~~~~~~~~~~;[\text{Differentiate both sides}]\\\\\implies dx = \dfrac{du}5\\\\\text{Now,}\\\\y = 2\cdot \dfrac 1  5 \displaystyle \int u^4 ~ du\\\\\\~~=\dfrac 25 \cdot \dfrac{u^{4+1}}{4+1} +C\\\\\\~~=\dfrac 25 \cdot \dfrac{u^5}5+C\\\\\\~~=\dfrac{2u^5}{25}+C\\\\\\~~=\dfrac{2(5x-3)^5}{25}+C

<h2>3)</h2>

\textbf{a)}\\\\y =  \displaystyle \int xe^{3x} dx\\\\\text{We know that,}\\\\ \displaystyle \int  (uv) ~dx = u  \displaystyle \int  v ~ dx -  \displaystyle \int \left[ \dfrac{du}{dx} \displaystyle \int ~ v ~ dx \right]~ dx\\\\\text{Let}, u =x~ \text{and}~ v=e^{3x}  .\\\\y=  \displaystyle \int xe^{3x} ~dx\\\\\\~~=  x\displaystyle \int e^{3x} ~ dx -  \displaystyle \int  \left[\dfrac{d}{dx}(x)  \displaystyle \int  e^{3x}~ dx \right]~ dx\\\\\\

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<h2 />
8 0
2 years ago
575 mL = ______ L<br>Please help me​
Lana71 [14]
575ml=0.575 liters
Cuz u divide the volume value by 1000
8 0
3 years ago
how many numbers between 650 and 780 leave remainders of 4 and 6 when divided by 7 and 11 respectively? pls help lol im desperat
Tanya [424]

Answer:

18 numbers between 650 and 780 leave remainders of 4 when divided by 7.

12 numbers between 650 and 780 leave remainders of 6 when divided by 11.

Step-by-step explanation:

1. Number 655 is the smallest number that leaves the remainder of 4 when divided by 7. Number 774 is the greatest number that leaves the remainder of 4 when divided by 7. So,

a_1=655\\ \\a_n=774\\ \\d=7\\ \\a_n=a_1+(n-1)d\Rightarrow 774=655+7(n-1)\\ \\7(n-1)=774-655\\ \\7(n-1)=119\\ \\n-1=17\\ \\n=17+1=18

2. Number 655 is the smallest number that leaves the remainder of 6 when divided by 11. Number 776 is the greatest number that leaves the remainder of 6 when divided by 11. So,

a_1=655\\ \\a_n=776\\ \\d=11\\ \\a_n=a_1+(n-1)d\Rightarrow 776=655+11(n-1)\\ \\11(n-1)=776-655\\ \\11(n-1)=121\\ \\n-1=11\\ \\n=11+1=12

7 0
4 years ago
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There are 46 children at the zoo. Twenty-nine students like popcorn and twenty like peanuts. Fifteen like both. How many student
lesya [120]

Answer:none

Step-by-step explanation:

You must mean 64 instead of 46.Because 29+20+15=64 but none would agree to dislike both popcorn not peanuts.

3 0
2 years ago
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