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S_A_V [24]
3 years ago
14

Derrick and Mark are brothers who live in the same house. Mark is at home, and Derrick is 5 miles away from home. Both boys begi

n riding their bikes at the same time. Derrick rides directly home at a constant rate of 15 mph, and Mark rides away from home at a constant rate of 18 mph. Let d represent distance from home, and t represent time in hours. Which system models this situation?
Mathematics
1 answer:
tia_tia [17]3 years ago
8 0
The system which models this situation is represented by the answer A.

A.
d = 5 − 15t
d = 18t
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If f(x)=-4x^2-6x-1 and g(x)=-x^2-5x+3, fine (f-g)(x)
NeX [460]

Answer:

\large\boxed{(f-g)(x)=-3x^2-x-4}

Step-by-step explanation:

(f-g)(x)=f(x)-g(x)

f(x)=-4x^2-6x-1,\ g(x)=-x^2-5x+3\\\\(f-g)(x)=(-4x^2-6x-1)-(-x^2-5x+3)\\\\(f-g)(x)=-4x^2-6x-1-(-x^2)-(-5x)-3\\\\(f-g)(x)=-4x^2-6x-1+x^2+5x-3\qquad\text{combine like terms}\\\\(f-g)(x)=(-4x^2+x^2)+(-6x+5x)+(-1-3)\\\\(f-g)(x)=-3x^2-x-4

5 0
3 years ago
Negative 4 is greater than or less than negative 1
kirill115 [55]
Negative 4 is less than negative 1
6 0
3 years ago
Read 2 more answers
A bag contains nine red balls, four green balls, and fifteen yellow balls. What is the probability of pulling out one red ball?
Aleksandr [31]

Answer:

32.1%

Did you type something in wrong?

Step-by-step explanation:

9+4+15=28 total balls

9=total red balls

total red balls/total balls= probability of pulling out one red ball

9/28

9÷28=32.1%

8 0
3 years ago
The cost for x number of students to attend an after school sporting event can be represented bu the functon C(x). If C(124) = 5
lara [203]
Alright! Given that C(x) is Cost(Students) = 558, we can eliminate:

2. 558 students paid to attend the event.
5. The event generated $124 from student revenue.

Now, in order to find the cost per student we simply divide 124 on both sides:

\frac{C(124)}{124} =  \frac{558}{124}

124 cancels on the left and 558/124 is 4.5 or $4.50. 

Since we just determined the cost of one student, we can eliminate 3.

To check if 124 students paid, we simply add the cost to the equation and check:

4.5(124) = 558

558 = 558 √

It checks out, so we determined that both 1 and 4 are correct.
7 0
3 years ago
Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using
AlladinOne [14]

Answer:

<u></u>

  • <u>a) P(X=1) = 0.302526</u>
  • <u>b) P(X=5) = 0.010206</u>
  • <u>c) P(X=3) = 0.18522</u>
  • <u>d) P(X≤3) = 0.92953</u>
  • <u>e) P(X≥5) = 0.010935</u>
  • <u>f) P(X≤4) = 0.989065</u>

Explanation:

Binomial experiments are modeled by the formula:

       P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}

Where

  • P(X=x) is the probability of exactly x successes

  • C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}

  • p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.
  • n is the number of trials
  • 1 - p is the probability of fail
  • there are only two possible outcomes for each trial: success or fail.

<u>a.) P (x=1)</u>

<u></u>

       P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526

<u>b.) P (x=5)</u>

     P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206

<u>c.) P (x=3)</u>

Using the same formula:

    P(X=3)=0.18522

<u>d.) P (x less than or equal to 3)</u>

  • P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

  • P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

  • P(X=4) = 0.059335
  • P(X=5) = 0.010206
  • P(X=6) = 0.000729

  • P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

<u>e.) P(x greather than or equal to 5)</u>

  • P(X≥5) = P(X=5) + P(X=6)
  • P(X≥5) = 0.010206 + 0.000729 =  0.010935

<u>f.) P(x less than or equal 4)</u>

  • P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)
  • P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
5 0
3 years ago
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