A group of 19 beavers get together to build a dam. They decide to divide into teams with 4 beavers on each full team. After they make as many full teams as possible, the rest of the beavers make a smaller team.

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

-------------

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

for such more question on  variables.

https://brainly.com/question/19803308

#SPJ11

Answer:

4.24 inches

Step-by-step explanation:

212/50

Answer:

4.24 inches

Step-by-step explanation:

To get the answer you divide 212 miles by 50 miles.

Answer: 87

Step-by-step explanation:

Four times a number decreased  by 5 is 67.Find the number.

Four times a number decreased by 5 is 67.

4x5=20

X-20=67

X=67+20

X=87

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Find more exercises on Interval notation;

https://brainly.com/question/17249352

#SPJ1

Distance between EF is 20.09 units.

By considering the given information

E=  (-4,2)

F= (16,4)

Distance between EF =

\(\sqrt{(16+4)^{2}+(4-2)^{2} } \\=\sqrt{400+4} \\=\sqrt{404} \\=20.09\)

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In coordinate geometry, the distance between two given points is calculated using the distance formula. The formula for calculating the separation between two points

Learn more about distance here

https://brainly.com/question/2854969

#SPJ1

Answer: C

Step-by-step explanation:

The closed circle on the left denotes "or equal to," and the open circle on the right denotes "less than."

So, it cannot be A, B, or D because they do not have \(\leq\) on the left and < on the right.

Only C has that option.

Answer is \(\frac{33}{8}\)

The length of the hypotenuse in this problem is given as follows:

h = 10.6 m.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The side lengths for this problem are given as follows:

7m and 8m.

Hence the hypotenuse is obtained as follows:

h² = 7² + 8²

\(h = \sqrt{7^2 + 8^2}\)

h = 10.6 m.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

Answer:

87124 + 14997 = 102121

Hope it helpz~ uh..

Carry on learning :)

Answer:

102121

Step-by-step explanation:

the approximate chance that a single randomly chosen student scores less than 525 on the GRE is 0.4279 or about 42.79%.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To answer this question, we need to standardize the score of 525 using the mean and standard deviation provided:

z = (x - mean) / standard deviation

where x is the score we want to find the probability for, mean is the mean score of the population, and standard deviation is the standard deviation of the population.

In this case:

z = (525 - 544) / 103 = -0.184

We can then use a standard normal distribution table or calculator to find the probability that a randomly chosen student scores less than 525, which is equivalent to finding the probability that a standard normal variable is less than -0.184:

P(z < -0.184) = 0.4279

Therefore, the approximate chance that a single randomly chosen student scores less than 525 on the GRE is 0.4279 or about 42.79%.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

Given that the cost of a computer program is $20 if 300 people buy them. For every $5.00 increase in price, 30 fewer people buy them. We need to find the relation between the price of computer programs and the number of people who will buy them.Relation between the price of computer programs and the number of people who will buy them can be represented in a table:Price per program .

Number of people who buy them$20 300$25 270$30 240$35 210$40 180$45 150$50 120Note that with each $5.00 increase in price, 30 fewer people buy the computer program.

Hence, the number of people who will buy the computer program will reduce by 30 with each $5.00 increase in price.

For instance, if the price increases from $20 to $25, the number of people who will buy it will reduce by 30 and be 270.

In conclusion, we can say that with every $5.00 increase in price, the number of people buying computer programs reduces by 30.

The relation between the price of computer programs and the number of people who will buy them can be represented in a table.

For such more question on computer

https://brainly.com/question/24540334

#SPJ8

Answer:

Slope (m): 1/2

Step-by-step explanation:

The rise is 1. As you can see on (-6,0), it goes up one and goes to the right 2 times. ( rise/run). This pattern continues as you can see on your graph.

movies 1.75 each

games 5.75 each

The total distance traveled by the particle from T=1 to t=5 is approximately 57.8 meter

What is velocity ?

Velocity is a vector quantity that describes the rate of change of an object's displacement with respect to time. It tells us how fast an object is moving and in what direction. The velocity of an object can be positive, negative, or zero, depending on the direction of its motion. The standard unit of velocity is meters per second (m/s) in the International System of Units (SI).

To find the total distance traveled by the particle from T=1 to t=5, we need to integrate the absolute value of the velocity function over this time interval.

First, we need to find the position function of the particle. We integrate the velocity function to get:

s(t) = ln|t| - (3/10)t^¹⁰/³+ 2t + C

To find the constant C, we use the fact that the position of the particle at T=1 is 8 m:

8 = ln|1| - (3/10)¹⁰/³ + 2(1) + C

C = 8 + (3/10) - ln(1) = 8.3

So the position function of the particle is:

s(t) = ln|t| - (3/10)t¹⁰/³ + 2t + 8.3

To find the total distance traveled by the particle from T=1 to t=5, we need to integrate the absolute value of the velocity function over this time interval:

distance = ∫|v(t)| dt from 1 to 5

Substituting the given velocity function v(t) = 1/t - t⅓ + 2, we get:

distance = ∫|1/t - t⅓ + 2| dt from 1 to 5

We can split the integral into two parts based on the sign of the integrand:

distance = ∫(2 - 1/t + t⅓) dt from 1 to 5 - ∫(-2 + 1/t - t⅓) dt from 1 to 5

Simplifying and integrating, we get:

distance = [2t - ln|t| + (3/4)t⁴/³] from 1 to 5 + [2t + ln|t| - (3/4)t⁴/³] from 1 to 5

distance = (10 - ln(5) + (3/4)(5⁴/³)) - (2 - ln(1) + (3/4)(1⁴/³)) + (10 + ln(5) - (3/4)(5⁴/³)) - (2 + ln(1) - (3/4)(1⁴/³))

distance = 2(ln(5) + 8/3) + 3/2(5⁴/³- 1)

Therefore, the total distance traveled by the particle from T=1 to t=5 is approximately 57.8 meter

To know more about velocity visit :-

https://brainly.com/question/80295

#SPJ1

Answer:

\(36\pi {a}^{3} \)

Step-by-step explanation:

Volume = \( \frac{4}{3} \times \pi \times (r)^{3} \)

\( \frac{4}{3} \times \pi \times {3a}^{3} \)

\( \frac{4\pi}{3} \times {3}^{3} \)

\( \frac{4\pi}{3} \times 27\)

\( \frac{4\pi}{3} \times (3(9))\)

\(4\pi \times 9\)

\(36\pi {a}^{3} \)

The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.

The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:

f(x) = (2x + 1)(x² - 8x + 8) + 5

Simplifying the above gives the following:

f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5

f(x) = 3x³ - 15x² + 8x + 13

Learn more about the function here:

brainly.com/question/5245372

Answer:

Step-by-step explanation:

7w + 72 + 24w

31w + 72

Answer:

x=6

Step-by-step explanation:

5/6-1/3=3/6 or 1/2 so 3/x=1/2 and since 3/6=1/2 x=6

The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

Learn more about mathematical operations at brainly.com/question/20628271

#SPJ1

Answer:

An example of an invertebrate are insects, crabs, spiders....

Step-by-step explanation:

Invertebrate Are animals that their legs are jointed.

Answer:

the snail

Step-by-step explanation:

Answer:

\(2 \frac{n}{ {m}^{2} } \)

Step-by-step explanation:

\( \frac{f}{a} = \frac{72}{6.1 \times 6.1} = \\ \frac{72}{37.21} = 1.93 \\ 2\)

Answer:

12km

Step-by-step explanation:

Let unknown= x

40 km = 3 2/3 hrs

xkm = 1 hr

cross multiplying

x =44÷ 3 2/3

=12 km

The ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated y-coordinates.

From the given linear functions, the ordered pairs that represents a function y in terms of x are  {(-2, -3),(1, 3),(1, 6) (9, 8}, (12, 11)) and {(-3, -5), (3, 2), (6, 5), (7, 9), (10, 16)}

Learn more on ordered pairs here: brainly.com/question/1528681

#SPJ1

Answer:

4x - 2y = -12

Step-by-step explanation:

4(3) - 2(12) = b

12 - 24 = b

-12 = b

4x-2y = -12

9514 1404 393

Answer:

  (d)  x-4

Step-by-step explanation:

If we assume your answer choices are ...

  (a) 5 -x = 5 -4 = 1

  (b) 1/2x = 1/2(4) = 2

  (c) x +1 = 4 +1 = 5

  (d) x -4 = 4 -4 = 0

Then the last choice (d) x -4 has the smallest value at x=4.

The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

For more questions on Payment .

https://brainly.com/question/27926261

#SPJ8

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

learn more about volume of prisms from

https://brainly.com/question/23766958

#SPJ1

Answer:

200 cm

Step-by-step explanation:

2*100= 200

Answer: 200 centimeters

Step-by-step explanation:

100 centimeters = 1 meter

? centimeters = 2 meters

100 x 2 = 200

200/1 = 200 centimeters

Answer:

15 ways

Step-by-step explanation:

girl 1 and boy 1

girl 2 and boy 1

girl 3 and boy1

girl 1 and boy 2

girl2 and boy 2

girl 3 and boy 2

girl 1 and boy 3

girl 2 and boy 3

girl 3 and boy 3

girl 1 and boy 4

girl 2 and boy 4

girl 3 and boy 4

girl 1 and boy 5

girl 2 and boy 5

girl 3 and boy 5