The sum of the speeds two trains is 717.6 miles per hour. If the speed of the first train is 6.4 mph faster than that of the second train, find the speeds
of each.
What is the speed of the first train?

Answer:

A) C = 1/96

B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Step-by-step explanation:

f(x,y) = C x (1+y)

A)

To find C, we need to integrate the volume under region bound by

0 <= x <= 4, and

0 <= y <= 4

This volume equals 1.0.

Find integral,

int( int(f(x,y),x=0,4), y = 0,4) = 96C

therefore C = 1/96

or

F(x,y) = x (1+y) / 96  ............................(1)

B)

P(x<=1, y<=1)

Repeat the integral, substitute the appropriate limits,

P = int( int(F(x,y),x=0,1), y = 0,1)

= 1/128 or 0.0078125

P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places

C)

P(x+y<=1)

From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.

It will be again a double integral, as follows:

P = int( int(F(x,y),x=0,1-y), y = 0,1)

= 5/2304

= 0.0021701 (to 7 decimals)

P(x+y<=1) = 5/2305, or 0.0021701 to 7 places

Answer:

product A

75%

67%

Product B

Step-by-step explanation:

I just found the percentage by dividing the amount of people who found relief into the whole

Hopes this helps please mark brainliest

The measure of three angles of triangular backyard are 28°, 31°  and 121°.

Given that, a home has a triangular backyard.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the measure of first angle be x.

The second angel of the triangle is 3 more than the first angel = x+3

The third angel is 9 more than four times the first angel = 4x+9

Using angle sum property of a triangle

x+x+3+4x+9 = 180°

⇒ 6x + 12 = 180

⇒ 6x = 168

⇒ x = 28°

So, x+3 = 31° and 4x+9 = 121°

Therefore, the measure of three angles of triangular backyard are 28°, 31°  and 121°.

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5th term of the sequence is -4

To find the 5th term in the sequence, we need to substitute n =  5 into the expression given

 \(a_5\) =  26- 6( 5)  

\(a_5\) =  26- 30

\(a_5\) = -4  

The formula given, an =  26- 6n, represents an  computation sequence with a common difference of-6.

This means that each term in the sequence is  attained by obtain 6 from the  former term.  

It's important to note that the formula is written in general form, meaning that it can be used to find any term in the sequence by simply plugging in the  matching value of  n.

 In this case, we were asked to find the 5th term, so we substituted n =  5 into the formula to get a5 = -4.

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Answer:

Thats not true

Step-by-step explanation:

12+15=27

27>20

27 is greater than 20 but your equation doesn't  equal 20

Answer:

4

Step-by-step explanation:

Answer: 128

Step-by-step explanation:

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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The slope of the line that passes through the points (7,-4) and (11,-4) is 0.

The slope of a line is found by using the formula:

slope = (change in y)/(change in x)

To find the change in y, subtract the y-coordinate of one point from the y-coordinate of the other point:

-4 - (-4) = 0

To find the change in x, subtract the x-coordinate of one point from the x-coordinate of the other point:

11 - 7 = 4

Now we can use the formula to find the slope:

slope = 0/4 = 0

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Step-by-step explanation:

yan po ang sagot ko dahil yan po ang pagkakaintindi ko

If each term in the sum a1+a2+a3...+an is  7 and the sum equals 350, C: 40 would be equal to n.

In equation form, it is:  

                  7s +  77t = 350

In this equation,

          s represents the number of 7's

          t represents the number of 77's

          thus, the number of terms i.e n = s + t =?

now solving the equation,

        7 (s + 11t) = 350

        7 (s + 11t) = 350

            s + 11t = 50

            s + 11t = 50

now, if  

       s=39     &      t =1  

then

         s + 11t = 50 -> 39 + 11 (1)  = 50

Since the number of terms n = s + t

        n = s + t

        n = 39 + 1

        n = 40

Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.

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Answer:

4 x 34 is greater than 34, since 4 is greater than 1.

Answer:

4 x 34 is greater than 34, since 4 is greater than 1.

Step-by-step explanation:

Answer:

x = 3.25 or 3 \(\frac{1}{4}\)

Step-by-step explanation:

The total length of the top side is equal to the total length of the bottom line. This means that:

x + 6.42 + 7.08 = 16.75

To find x, rearrange to make it the subject by subtracting the two on the side of x from the opposite side:

x = 16.75 - 6.42 - 7.08

x = 3.25

x = 3 \(\frac{1}{4}\)

Hope this helps!

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Answer:

Step-by-step explanation:

The next number is 110

Answer:

Option a is the correct answer

Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

Answer:

\({ \boxed{ \rm{y = 3x - 11}}}\)

Step-by-step explanation:

• Let the equation be:

\({ \tt{y = 3x + m}}\)

• when x is 1, y -8

\({ \rm{ - 8 = 3 + m}} \\ \\ { \rm{m = - 11}}\)

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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Answer : 0.99

Explanation :  15 * 6.6/100 For The Tax.

Total : 15.99

Answer:

c

Step-by-step explanation:

Answer:

x = 2 ± √34/5

Step-by-step explanation:

Move terms to the left side.

5x^2 - 4x = 6

5x^2 - 4x -6 = 0

Identify a, b, and c before plugging them into the quadratic formula.

a = 5

b = -4

c = -6

x = -(-4) ± √(-4)^2 - 4 * 5(-6)/2 * 5

Then simplify.

Answer:

Step-by-step explanation:

The distance travelled by both Evelyn and Sarah is 30 miles.

Given,

The speed travelled by Evelyn = 30 mph

Time taken by Evelyn to cover a distance = 20 minutes

Speed travelled by Sarah = 60 mph

We have to find the distance travelled by both of them.

Speed = distance / time

Then,

Distance = speed x time

Lets take x as the distance.

Then,

36 × (x + 20) = 60x

36x + 720 = 60x

60x - 36x = 720

24x = 720

x = 720/24

x = 30

That is,

The distance travelled by both Evelyn and Sarah is 30 miles.

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Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

Answer:

Least common multiple = 150

Step-by-step explanation:

The least common multiple is defined as the smallest multiple that two or more numbers have in common.

We can find the least common multiple by listing the multiples of both numbers:

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Multiples of 50:

50, 100, 150

Thus, 150 is the least common multiple of 15 and 50.

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer: it will take 5 days

Step-by-step explanation:

on the 5th day joey will be opening his 5th carton of milk and is 4th box of cereal

We can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability.

What is probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The theoretical probability of rolling a 5 on a fair die is 1/6, which means that if the die is rolled many times, we would expect to see a 5 about 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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We might say that Maya's experimental probabilities oscillate about the theoretical probability, but after more trials, the experimental probabilities ought to converge to the theoretical probability.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

A fair die has a theoretical probability of rolling a 5 of 1/6, therefore if the die is rolled several times, we can anticipate seeing a 5 roughly 1/6 of the time.

For the first 100 trials, Maya rolled a 5 on 25 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 25/100

experimental probability = 0.25

So, in the first 100 trials, Maya's experimental probability of rolling a 5 was 0.25.

For the first 200 trials, Maya rolled a 5 on 30 of those trials. The experimental probability of rolling a 5 in this case is:

experimental probability = number of 5's rolled / number of trials

experimental probability = 30/200

experimental probability = 0.15

So, in the first 200 trials, Maya's experimental probability of rolling a 5 was 0.15.

Comparing these experimental probabilities to the theoretical probability, we see that after 100 trials, Maya's experimental probability of rolling a 5 (0.25) is higher than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 100 trials was somewhat biased in favor of rolling a 5.

On the other hand, after 200 trials, Maya's experimental probability of rolling a 5 (0.15) is lower than the theoretical probability (1/6 ≈ 0.167). This suggests that Maya's sample of 200 trials was somewhat biased against rolling a 5.

Overall, we can conclude that Maya's experimental probabilities fluctuate around the theoretical probability, but over a larger number of trials, the experimental probabilities should converge towards the theoretical probability. This is known as the law of large numbers, which states that as the number of trials or observations increases, the experimental probability will tend to approach the theoretical probability.

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Basic info:

4 (x) hours = 6 logs (y), need keep fire burning for 18 hours.

Problem:

4x = 6y

what y = 18x?

8x = 12y

16x = 24y

18x = 26y

Answer:

26 logs