Traviling upstream on the Mississippi River, a barge travels 56 mi in 7 h. Downstream, it travels the same distance in 4 h. Find the rate of the barge in still water and the rate of the current

Answer: Angelo is 13 years old.

Aaron is 15 years old

Alfred is 34 years old

Step-by-step explanation:

Let x represent the age of Angelo.

Let y represent the age of Aaron.

Let z represent the age of Alfred

The sum of three guys ages is 62. It means that

x + y + z = 62 - - - - - - - - - - -1

Angelo is two years younger than Aaron. It means that

x = y - 2

Alfred is four years older than twice Aaron's age. It means that

z = 2y + 4

Substituting x = y - 2 and z = 2y + 4 into equation 1, it becomes

y - 2 + y + 2y + 4 = 62

4y + 2 = 62

4y = 62 - 2 = 60

y = 60/4 = 15

x = y - 2 = 15 - 2

x = 13

z = 2y + 4 = 2 × 15 + 4

z = 34

Answer:

the answer would be C. The mean would increase.

Step-by-step explanation:

The mean has increased, the correct option is C.

Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.

The total number of students is 19.

The outlier is 81

An outlier is a number that is different from the other set of numbers, it is obtained due to variability in the observation or due to experimental error.

The mean including the outlier of 81 equals 94.

For the mean including the outlier, it can be observed that the outlier is the left outlier or the smallest number.

Let x represent the sum of all the test scores

x / 19 = 94

x = 94 * 19

x = 1786

The sum without the outlier is 1786 - 81 = 1705

The mean without the outlier is

= 1705 / 18

= 94  13 /18

This is greater than 94.

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Final answer:

To solve the problem, set up a system of equations representing the total number of chickens and the total cost. Solve the system using substitution or elimination method to find the number of Americana and Delaware chickens that Allysa bought.

Explanation:

Allysa spent a total of $35 to purchase 12 chickens. Let's denote the number of Americana chickens as 'x' and the number of Delaware chickens as 'y'. The cost of Americana chickens is $3.75 each, while the cost of Delaware chickens is $2.50 each. Based on this information, we can establish two equations:

x + y = 12 (equation 1, representing the total number of chickens)

We can solve this system of equations using substitution or elimination method. Let's use substitution:

Therefore, Allysa bought 4 Americana chickens and 8 Delaware chickens.

Alyssa purchased 4 Americana chickens and 8 Delaware chickens. By solving the system of equations, we determined the number of each type of chicken. At the end of the first week, she expects to take in $22.5  from selling eggs.

To determine the number of Americana chickens, A, and the number of Delaware chickens, D, Alyssa purchased, we set up a system of equations based on the given information:

Now, to solve the system, we can use substitution or elimination. Let's use substitution:

So, Alyssa purchased 4 Americana and 8 Delaware chickens.

To determine Alyssa's expected income from selling eggs at the end of the first week:

Therefore, Alyssa expects to take in $22.5 at the end of the first week from selling eggs.

Complete Question:

Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.

Answer:

12 cups

Step-by-step explanation:

If the size of the bag decreased by 20%, so will the number of cups held.

Number of cups held before the change = 15 cups

If the number of cups held after the 20% reduction in the size of the bag

= (100 - 20)% × 15

=80% × 15

= 12 cups

The new bags will hold 12 cups.

The old bags held 15 cups of popcorn so, the new bags holds 12 cups of popcorn and this can be determined by using the unitary method.

Given :

The unitary method can be used to determine the total number of cups of popcorn the new bag can hold.

Given that the old bags held 15 cups of popcorn, so, it is 100% capacity of the old bag. So, according to this capacity, the new bag can 80% of cups of popcorns that is:

[tex]=\dfrac{80}{100}\times 15[/tex]

Multiply 80 by 15 in the above expression.

[tex]=\dfrac{1200}{100}[/tex]

Now, divide 1200 by 100 in the above expression.

= 12 cups of popcorn

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Answer:

x=22.5

Step-by-step explanation:

BM||DT

Using Intercept theorem/Intercept theorem

[tex]\frac{6}{6+15} =\frac{9}{9+x}[/tex]

6(9+x)=9*21

54+6x=189

6x=135

x=22.5

At least I think so

Answer:the equations are

x + y = 8

20x + 110y = 340

Step-by-step explanation:

Let x represent the number of commercials on which Alexa's songs were played.

Let y represent the number of movies on which Alexa's songs were played.

The total number of movies and commercials on which Alexa earned is 8. It means that

x + y = 8 - - - - - - - - - - - -1

Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that

20x + 110y = 340 - - - - - - - - - - - -2

Answer:

variables:

c= the number of commercials

m= number of movies

system of equations:

20c+110m= 340

c+m= 8

Answer:

  y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

  A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

  C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

  k·10 = 2π

  k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

  y = 4cos((π/5)x) +3

To find a function that matches a given graph, the amplitude, frequency, and phase shift must be determined. The amplitude is calculated by determining the maximum and minimum values of y, the frequency is found by comparing the distances in the cycles, and the phase shift is calculated by looking at the middle of the oscillation.

In order to find a function that matches the graph given, we need to determine certain aspects of the waveform such as the amplitude, frequency, and phase shift. This is done through carefully analysing the graph. In general, A resembles the amplitude or the 'height' of the wave. This can be determined by calculating half the distance between the maximum and minimum values of y. The coefficient k is linked to the frequency of the function, which can be figured out by the distance between alike points in the cycle (like peak to peak, or trough to trough). And finally, C corresponds to any vertical shift of the function which can be understood by checking the 'middle' of the oscillation. If the wave seems to be shifted to the right or left of the y-axis, then you would use a phase shift in the sine or cosine function. Remember, cosine and sine functions are similar in shape, but a cosine waveform begins at a peak, while a sine waveform begins at zero.

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The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

or approximately 135.7 km/h.

Answer:

Another way to decompose the number would be

43  taking the 4 of the left with tens like 40 ( 4*10) and 3 of the right as three separate ones ( 3*1= 3) .Adding 10s four times with  three one times would make 43

Final answer:

The student's question deals with decomposing numbers into tens and ones and relates to the concept of powers of ten in mathematics. Powers of ten notation is foundational in understanding place value, large, and small numbers. By breaking down numbers into tens and ones, students can grasp numerical values more effectively.

Explanation:

The question pertains to the mathematical concept of decomposing numbers into tens and ones using a ten-frame and involves powers of ten. In mathematics, numbers can be broken down into tens and ones to understand their value better. It's essential to note that each place in our numbering system is ten times greater than the place to the right of it. This is part of the reason we use powers-of-ten notation.

Decomposing Numbers

When decomposing a number like 24, for example, we can break it down into two tens (20) and four ones (4). If we used a ten-frame, we would fill in two full ten-frame grids to represent the tens and then add four individual marks to represent the ones.

Understanding Powers of Ten

When we discuss powers of ten, we're talking about how the counting system is structured, with each place value being ten times greater than the one before it. The digital numbering system got started because humans have ten fingers and counted with them, leading to an increase by tens.

A positive exponent, like 10³, tells us to multiply the base (10) by itself the number of times indicated by the exponent (3), which results in 1000. On the other hand, a negative number as the power indicates a division, so a power like 10⁻¹=0.1. If we have 10⁻⁴, it means 0.0001, which is ten times smaller than 0.001 (10⁻³).

When dividing by powers of ten, we move the decimal point to the left by the number of zeros indicated by the power. This process simplifies understanding large and small numbers by expressing them in terms of powers of ten or powers of one thousand for very large numbers.

Answer: 162  sq. yds.

Step-by-step explanation:

Given : A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd.

Then , Area of rectangle = length x width

= 11 yd  x 17 yd = 187 sq. yds.

Area of square = (side)²  

= (5 yd)² = 25  sq. yds.

Now , the area of the region inside the rectangle that surrounds the square will be Area of rectangle - Area of square

= 187 sq. yds.- 25  sq. yds.

=162  sq. yds.

Hence, the area of the region inside the rectangle that surrounds the square is 162  sq. yds. .

Answer:

For 612 copies both companies will charge the same amount.

Step-by-step explanation:

Consider the provided information.

let x represents the number of copies and y represents the total charge.

Company A rents copy machines for $300 a month plus $0.50 per copy.

[tex]y = 300 + 0.5x[/tex]

Company B charges $600 a month plus $0.01 per copy.

[tex]y=600 + 0.01x[/tex]

We need to determine the number of copies for which two companies charge the same amount, so equate the equations as shown.

[tex]300 + 0.50x = 600 + 0.01x\\0.49x=300\\x\approx612.244[/tex]

The Approximate value of x to nearest whole number is 612.

Hence, for 612 copies both companies will charge the same amount.

Answer:

Step-by-step explanation:

A female bunny gained three pounds per. It means that the total number of pounds that the female bunny gained in 6 weeks would be

3 × 6 = 18 pounds.

A male bunny gained 8 pounds per week. It means that the total number of pounds that the male bunny gained in 6 weeks would be

8 × 6 = 48 pounds.

Therefore, the number of pounds that the male bunny gained more the female bunny would be

48 - 18 = 30 pounds

Step-by-step explanation:

Female Bunny: Doe

Male Bunny: Buck

A doe gained three lbs per week for six weeks.

3 x 6 = 18

A buck gained eight lbs per week for six weeks.

8 x 6 = 48

How many more lbs did the buck get than the doe?

48-18= 30

Answer:

The male bunny gained thirty more pounds than the female bunny.

The buck gained 30 more lbs than the doe.

Answer:

Park is 5 miles from Billy's home.

Step-by-step explanation:

Given:

Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.

Now, to find the distance from park to Billy,s home.

Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.

So, the time = (9.30 - 9.00) = 30 minutes

[tex]=\frac{30}{60}[/tex]  [tex]=0.5\ hour.[/tex]

Speed = 10 miles per hour.

Now, to get the distance from park to Billy's home we put formula:

[tex]Distance=Speed\times Time.[/tex]

[tex]Distance=10\times 0.5[/tex]

[tex]Distance=5\ miles.[/tex]

Therefore, park is 5 miles from Billy's home.

Answer:

The bus traveled 720 miles with constant speed.

Step-by-step explanation:

Given,

Distance = 336 miles

time = 7 hrs

We have to find out the distance traveled by the bus in 15 hours with constant speed.

Solution,

Since we know that the speed is equal to distance divided by time.

So the equation can be framed as;

[tex]speed=\frac{336}{7}=48\ mi/h[/tex]

Now time = 15 hrs

Distance traveled is equal to speed multiplied with time.

So the equation can be framed as;

[tex]Distance\ traveled=48\times15=720\ miles[/tex]

Hence The bus traveled 720 miles with constant speed.

Answer:

B. A continuous continuous data set because there are infinitely many possible values and those there are infinitely many possible values and those values cannot be counted values cannot be counted

Step-by-step explanation:

Given that the  volume of cola in a can is 12.1 oz

We have to find out whether discrete or continuous.

We can say a random variable is discrete if it takes values which have one to one correspondence with the set of natural numbers.

continuous if a one to one correspondence with set of natural numbers cannot be established.

In our case, we have volume of cola as 12.1 oz.  Between two readings say,12.1 oz and 12.15 oz. there may be infinite other values which the volume can take

i.e. this is a continuous data.

B. A continuous continuous data set because there are infinitely many possible values and those here are infinitely many possible values and those values cannot be counted values cannot be counted

is right answer

The volume of cola in a can, measured as 12.1 oz, is an example of continuous data because it could theoretically take any value in a certain range, unlike discrete data which can only have certain distinct values.

The volume of cola in a can being 12.1 oz represents continuous data. This is because continuous data can take on any value within a certain range or interval. In this case, the volume of the cola in the can could theoretically have been any number between certain limits, for example, 0 to 12.2 oz. This differs from discrete data, which can only take certain distinct or separate values, such as the number of cans of cola you might buy (1,2,3, etc.).

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Final answer:

The minimum number of hours that a car share needs to be used per year to make Company B a better deal is B. 6.

Explanation:

To determine the minimum number of hours that a car share needs to be used per year to make Company B a better deal, we can set up an equation with the costs of each company. Let h represent the number of hours:

Company A's cost: $110 + $10h

Company B's cost: $125 + $7h

We need to find the point at which Company B's cost is less than Company A's cost. Solve the inequality:

$125 + $7h < $110 + $10h

$15 < $3h

Divide both sides by 3 to isolate h:

5 < h

The minimum number of hours that a car share needs to be used per year to make Company B a better deal is 6.

Answer:

1 minute = 1080 - 960 = 120 m

5 minutes = 5400 - 4800 = 600 m

8 minutes = 8640 - 7680 = 960 m

Step-by-step explanation:

I think the easiest way is to just see how far they get at each time.  So I'm going to go one horse at a time.

16 m/s

1 minute = 60 seconds, every second is 16 meters so 16 m/s * 60 s = 960 m

5 minutes = 300 seconds so 16 m/s * 300 s = 4800 m

8 minutes = 480 seconds, 16 m/s * 480 s = 7680 m

I also want to point out that unites cancel out.  m/s * s is kinda like variables so the seconds being multiplied by m/s cancels witht eh seconds in the denominator.

Now the next horse

18 m/s

1 minute totals to 1080 m

5 minutes = 5400 m

8 minutes = 8640 m

Now we take the differences of each time

1 minute = 1080 - 960 = 120 m

5 minutes = 5400 - 4800 = 600 m

8 minutes = 8640 - 7680 = 960 m

Another way to do this is to take the difference of speed and then multiply that by the time.  so 18-16 = 2, then multiply each time by 2.  For me it just makes more intuitive sense the way I showed.  

Answer:

Lesser than 6.9 minutes

Step-by-step explanation:

Let m represent the number of minutes of phone use with either plan A or plan B.

In plan A, the customer pays a monthly fee of $35 and then an additional 9 cents(9/100 = $0.09) per minute of use. This means that the total cost of m minutes would be

0.09m + 35

In Plan B, the customer pays a monthly fee of $55.70 and then an additional 6 cents(6/100 = $0.06) per minute of use. This means that the total cost of m minutes would be

0.06m + 55.70

Therefore, for the amounts of monthly phone use for which Plan A will cost less than Plan B, it becomes

0.09m + 35 < 0.06m + 55.70

0.09m - 0.06m < 55.70 - 35

0.03m < 20.7

m < 20.7/3

m < 6.9

Answer:

He paid = $20,500

Step-by-step explanation:

Let the amount he bought the car originally be X

so from the statement,

(2/5)*X + $200 = $8,400

(2/5)*X = $8,400 - $200

solving for X

X = $8200 * 5/2

X = $20,500

Answer:

a is the right answer atleast that's what I think

Answer:

D.

Step-by-step explanation:

neither of these is a mathematical statement. P only mentions the word math and Q has nothing to do with math.

Answer:

the answer is 16ft

step-by-step explanation:

in order to make a triangle with non-zero area, the sum of the shorter two sides must be greater than the longest side.

here, 4 + 4 > 7, so the lengths can form a triangle.

The correct answer was given: Brain

7+8= 15

hope this

The correct answer was given: Brain

36 cm is the final : )

The Answer is

5 by 9

Answer:

Explanation:

The range of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).

To figure out the range of a function, you first must figure out the domain.

The domain of the function   [tex]y=\sqrt[3]{x}[/tex]  is all real values, since the cube root function is defined for all the real numbers.

Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of   [tex]y=\sqrt[3]{x}[/tex]  is all real numbers.

A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.

Thus, the range of the translated function is (-∞, ∞).

That can also be written as {y|y is a real number}, which is read "y such that y is a real number", and is the last choice of the list.

Answer:

6sqrt(2) units (exact form)

= 8.49 units (3 sf)

Step-by-step explanation:

sqrt[(-1-5)²+(6-0)²]

sqrt[(-6)² + 6²]

sqrt(36 + 36)

sqrt(72)

= 6sqrt(2) units (exact form)

= 8.49 units (3 sf)

Answer:

3

Step-by-step explanation:

Recall that the full circumference of a circle can be represented by an angle of 360°.

In our case, we are asked to find the arc AB on the circumference of a circle that is represented by an angle of only 20°

hence the fraction of the circumference that is represented by arc AB

= 20° / 360°

= 1/18

we can thus say that the length of AB is 1/18 of the total circumference

Arc Length of AB

= (1/18) of total circumference

= (1/18) x 2π x radius

= (1/18) x 2π x 27

= 3π units

Answer:

3π Radian

Step-by-step explanation:

[tex]we \: have \: \: \: s = r \alpha \\ here \: s = arc \: length \\ r = radious \: of \: circle \\ \alpha = centre \: angle \: of \: current \: circle \\ so \\ s = 27 \times 20 \\ \: \: \: = 540 \\ \: \: \: \: \: = 540 \times \frac{\pi}{180} \\ \\ \: \: \: \: = 3\pi \: radian[/tex]

.

Answer:

This is known as Data dredging.

Step-by-step explanation:

In order for any statistical analysis to be significant, a researcher has to first generate a hypothesis.  

Data dredging is trying to uncover patterns in data that can be presented statistically without devising a clear hypothesis by use data mining.  It is also referred to as data fishing or p-hacking.  

In this case any correlation (relationship between cause-effect)will be purely by chance.

Therefore, the investigator is Data dredging

Answer:

If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.

It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.

A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.

Step-by-step explanation:

If it is possible for the student to wear a hand glove while transporting the chemicals to the other room, and use her other hand to open doors and use elevators.

It is also better if she could with her teammate and they could share responsibilities such that one of them carries the solutions while the other opens doors and uses the elevator.

A less breakable or plastic bin could have been used to convey the solutions to the other room to prevent the use of bare hand from contacting the glassware.

Answer:

4

Step-by-step explanation:

in similarity the ratio of the similar sides is the same i.e

10/5 =8/x

2x=8

x= 4

Answer:

The answer is 1/7

To add fractions, find the LCD and then combine

Answer:c is the correct answer

Step-by-step explanation:

A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x

where y is the number of dollars charged and

x is the number of minutes the repair person is on the job.

Therefore, to determine the number of minutes that it would take for the cost of repair to reach $130, we would substitute y =130 into the given model. It becomes

130 = 47.38 + 0.617x

0.617x = 130 - 47.38 = 82.62

x = 82.62/0.617 = 134 minutes

Answer:

a

Step-by-step explanation: