A boat travels 26 miles up a river in the same amount of time it takes to travel 38 miles down the same river. If the current is 3 mph, what is the speed of the boat in till water?

x + (x + 1) = 75

2x + 1 = 75

2x = 74

x = 37

75 - 37 = 38

You can check by substituting the product for the value of x.

37 + 37 + 1 = 75

The two consecutive integers whose sum is 75 are; 37 and 38.

If two consecutive integers sum up to become 75.

We can represent the first number as = x and

the second number as = (x + 1).

The sum of both of the numbers = 75.

therefore, x + (x + 1) = 75.

Dividing both sides of the equation by 2; we have;

x = 37

x + 1 = 38.

Ultimately, the two consecutive integers are; 37 and 38.

Read more:

https://brainly.com/question/18370359

Answer:

The value of rate of change in the equation [tex]T(d)=37.69d+60.22[/tex] is 37.69.

Step-by-step explanation:

Given the equation that models the total cost(T) is:

[tex]T(d)=37.69d+60.22[/tex]  where d is the drink you purchase.

To determine the rate of change:

1. An equation must be into the Slope-intercept form (y=mx+b).

2. m is the slope (rate of change) of the linear function.

3. b is the y-intercept of the linear function (y- intercept is where the line crosses the y-axis).

Since, the given equation is in the linear form i.e, [tex]T(d)=37.69d+60.22[/tex]

The rate of change(m) of the given equation is, 37.69.

The length of ribbon needed to make 9 bows is 9 times the amount of ribbon needed for one bow, expressed mathematically as 9*x given 'x' is the length of ribbon for one bow.

Based on your query, there appears to be a detail missing, which is the length of the ribbon needed to make one bow. Suppose we denote that length as 'x' units. To find the total length necessary for making 9 bows, we would simply multiply that length by 9. In mathematical terms, this would be expressed as 9*x. So if it takes x units of ribbon to make one bow, it will take 9*x units of ribbon to make 9 bows.

http://brainly.com/question/11319098

#SPJ2

Due to a typo, the exact length of ribbon per bow is unspecified. Assuming a length of [tex]\( x \)[/tex] per bow, for 9 bows the total needed would be [tex]\( 9x \)[/tex] This is akin to scaling up costs for making multiple items, similar to the production cost examples provided.

It seems there is a typo in the initial fraction of ribbon used per bow, as it is not provided in the question. Assuming the fraction provided is the one we would work with, let's say it takes [tex]\( x \)[/tex] of a ribbon to make one hair bow. To find out how much ribbon is needed to make 9 bows, we multiply [tex]\( x \)[/tex] by 9. Therefore, the total amount of ribbon required for 9 bows would be [tex]\( 9x \)[/tex].

Going by the example information given, if we compare it with the cost of manufacturing goods, we can draw on the parallel of calculating the cost to produce multiple items. For example, if pants finishing costs 49 cents for 7 pairs, and we want to calculate for 9 pairs, we would set up a proportion or use unit rate to find the answer. Though this example doesn't directly relate to the ribbon question, it illustrates the process of scaling up a unit quantity to a larger quantity, which is a common mathematical operation in both scenarios.

Answer:

the answer is a c and d

Step-by-step explanation:

It will take 4 minutes to rotate 1º because 15 divided by 15 is one (to get 1º) and 60 (1 hour) divided by 15 is 4.

Swimmers: 50 children ÷ 12 = 4.2  (you can't have a decimal so you must round up)

5 adults are need.

Dancers: 32 children ÷ 15 = 2.1  (you can't have a decimal so you must round up)

3 adults are need.

Minimum number of adults needed is: 5 for swimmers + 3 for dancers = 8 adults

-1 1/8 because -9/8 is equal to [tex]-\frac{9}{8}[/tex] so just make it a improper fraction, pretend the negative is not there then add the negative at the end

-hope this helps :D

To round 12,387 with the thousands place underlined, we look at the digit to the right (3) and, since it is less than 5, we round down by keeping the 2 unchanged and turning all the digits to its right to zeros, which gives us 12,000.

Since the next digit (3) is less than 5, we do not increase the value of the underlined digit. Thus, we keep the 2 as it is and change all the digits to the right of it to zeros, resulting in the rounded number 12,000.

This concept is similar to the general principle applied when rounding numbers, which involves looking at the digit immediately to the right of the target place value. If it's 5 or greater, we round up. Otherwise, we round down. Examples of rounding numbers in different situations include:

Significant figures: Rounding an answer like 2,085.5688 to five significant figures would result in 2,085.6 because the first digit to be dropped is greater than 5.

Limiting the final answer to a certain place value: When adding 6527.23 and 2, the answer must be reported as 6528 because the digit 2 has no decimal places that would be significant, so we can only report to the ones place.

When working with calculations such as 119.902, if we need to limit our answer to tenths based on significant figures, we round down to 119.9.

just think of it like this  6 x (30 - 3) so then it turns into 6 x 27 which is 162 :) I hope this helped :))

Answer: 1)100ways and 2)90ways

Step-by-step explanation:

Given :-The 10 students who completed a special flying course are waiting to see if they will be awarded the one Distinction or the one Merit award for their efforts.

Ways can the two awards be given if the same student can receive both awards (i.e repetition is allowed)

=10×10=100ways

Ways can the two awards be given if the same student cannot receive both awards(i.e. repetition is not allowed)

=10×9=90ways

Final answer:

The number of ways two awards can be given out to 10 students is 100 when the same student can win both awards, and 90 when different students must win each award.

Explanation:

The student's question deals with the number of ways two awards can be given out to a group of 10 students under two different scenarios: one where the same student can receive both awards, and the other where the same student cannot receive both awards. This is a problem of permutations and combinations, a fundamental concept in probability and statistics.

Scenario 1: Same Student Can Receive Both Awards

In the first scenario, the same student can receive both the Distinction and the Merit award. Since there are 10 students and each student can potentially receive each of the two awards, we have 10 choices for the Distinction award and 10 choices for the Merit award. The total number of ways the two awards can be given out is simply the product of these two numbers:

10 (for Distinction) × 10 (for Merit) = 100 ways

Scenario 2: Different Students Receive Awards

In the second scenario, the same student cannot receive both awards. This means that once a student has been given one award, they cannot receive the other one. For the Distinction award, there are still 10 possible students. However, for the Merit award, there are only 9 remaining choices since the Distinction awardee cannot be considered:

10 (for Distinction) × 9 (for Merit) = 90 ways

( - 6, 0).(2, 0 ) , vertex = ( - 2, - 16)

to find the x-intercepts set f(x) = 0

x² + 4x - 12 = 0

(x + 6)(x - 2) = 0 ( equate each factor to zero and solve for x )

x + 6 = 0 ⇒ x = - 6

x - 2 = 0 ⇒ x = 2

x- intercepts are ( - 6, 0),(2, 0)

given the quadratic in standard form : y = ax² + bx + c

the x-coordinate of the vertex = - [tex]\frac{b}{2a}[/tex]

here a = 1 , b = 4 and c = - 12

x- coordinate of vertex = - [tex]\frac{4}{2}[/tex] = - 2

substitute this value into the equation for y-coordinate

x = - 2 → y = 4 - 8 - 12 = - 16

vertex = ( - 2, - 16)

Given that speed of the cyclist = 36 kilometers per hour.

Now question says to find the speed in meters per second.

We know that 1 kilometer = 1000 meter

and 1 hour = 3600 seconds

so to convert 36 kilometers per hour into meter per second, we will multiply 36 by 1000/3600

36*1000/3600

=36*10/36

=10

Hence final answer is speed = 10 meters per second.

That 10 meters per second means cyclist will travel 10 meters in 1 second.

Now to find distance travelled in 5 seconds, we just need to multiply 10 and 5

So the final answer will be 10*5 or 50 meters.

Add 16 to 1 9/16 that will then be 25/16 then you divide 5 from 25 that equals 5 so that is your answer

the original price of the sofa was 727.26

77 - 3x = 5

subtract 77 from both sides : -3x = -72

divide by -3 on both sides to get x by itself : x = 24

The answer is that Mia has 24 friends (x = 24)

You find the highest number that can divide into all of them without leaving any with a remainder.

Hope this helps.

u have to multiply the three numbers till u get the GCF

correct me if im wrong

have a blessed day!

There are 259 kids on all 7 buses.

Answer:

open

Step-by-step explanation:

Inflation is the term used when an increase in the money supply reduces the purchasing power of money and causes prices to rise.

Um, I'm not directly sure what you mean but if its 5-2 then it makes 3.

I don't get this question. But, if its 5 - 2 it is 3.

Hope this helps! :)

Answer:

$5

Explanation:

Since Jerry walked the dog from 6:40am to 7:30am, the total minutes that he walked the dog was 50 minutes. Also a note, an hour is 60 minutes.

Since he is paid at a rate of $6 per 60 minutes, we can make a proportion.

   660=x50

From here, you have to solve for x. So cross multiply, and then simplify.

   60x=50⋅6

   60x60=50⋅6/60

   60x60=50⋅6/60

   x=5⋅6/6

   x=5

So the answer is $5.

Jerry earned about $76.98 for the day.

Jerry walked a dog from 6:40 am to 7:30 pm. To calculate how much he earned, we need to determine the total number of hours he worked.

First, we convert the end time into military time, which is 19:30.

Subtract the start time, 6:40, from the end time, 19:30.

Calculation:

Now, we use the rate of $6 per hour to calculate his earnings:

Earnings = Total hours * Rate per hour

Earnings = 12.83 hours * $6/hour = $76.98

Since Jerry worked a fraction of an hour, we included the approximate earnings up to two decimal places.

So, Jerry earned about $76.98 for the day.

Answer:

Step-by-step explanation:

Solution in given attachment.

the product is always the same:

1440

The smallest possible product using the digits 2, 3, 5, 6, 8 is 1440.

To do this, we’ll arrange the digits in ascending order:

2 < 3 < 5 < 6 < 8

Hence, the smallest number formed using these digits is 23568.

Now let’s calculate the product:

2*3*5*6*8 = 1440

So, the product is always the same: 1440.

Whether you arrange the digits in ascending or descending order, the product remains unchanged because multiplication is commutative (i.e., the order of multiplication doesn’t matter)

Answer: Our required decimal expansion would be[tex]1.\bar{240}[/tex]

Step-by-step explanation:

Since we have given that

[tex]1\dfrac{80}{333}[/tex]

We need to write in decimal form:

First we change the mixed fraction into improper fraction:

[tex]\dfrac{333\times 1+80}{333}=\dfrac{413}{333}\\\\=1.240240...............\\\\=1.\bar{240}[/tex]

Hence, our required decimal expansion would be[tex]1.\bar{240}[/tex]

This is placed at the thousandth place

(i think that is what you wanted me to answer..?)

hope that helps :)

63 is your answer

Check:

Multiply: 3 x 2 = 6

Check that it is greater than 60, less than 70: 60 < 63 < 70

~Rise Above the Ordinary

Answer:

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5

Step-by-step explanation:

2a + 4c = 38

3a + 3c = 40.5

To solve for the value of a and c in these equations. We solve the simulatenous equation by substitution method.

2a + 4c = 38 ..........eqn1

3a + 3c = 40.5 ............eqn2

Step 1, Find the value of a in eqn1

2a + 4c = 38

2a = 38 - 4c

a = (38-4c)/2

a = 19 - 2c

Step 2, subtitle the value of a in eqn2 to get the value of c.

3a + 3c = 40.5

3(19-2c) + 3c = 40.5

57 - 6c +3c = 40.5

57-40.5 = 6c -3c

16.5 = 3c

c = 16.5/3

c = 5.5

Step 3, subtitle the value of c in eqn1 to get the value of a.

2a + 4c = 38

2a + 4(5.5) = 38

2a + 22 = 38

2a = 38-22

2a = 16

a = 16/2

a = 8

Therefore:

Adult ticket = $8

Child ticket = $5.5

a = 8 and c = 5.5

Answer:

it is right

Step-by-step explanation:

Yes, you are correct.  A negative number times a positive is a pos, and 4 times 12 is 48. Neg times a neg is a pos, and 48 times 3 is 144.