a cardboard box in the shape of a rectangular prism has the dimensions shown. the volume of the box is 60 cubic inches. find the length, width, and height of the box.

Answer:

p = 3x

Step-by-step explanation:

p² = 9x² = 3² *x²

p² = (3x)²

p = 3x

The total Messages that Tammy, Felipe, and David sent are 30, 50, and 45 messages respectively.

Let's denote the number of text messages sent by Tammy as x, Felipe as y, and David as z. Based on the information given, we have:

y < x and z = 3y.

The total number of messages they sent is x + y + z = x + y + 3y = 4y + x.

Since the total number of messages sent is not specified, we can choose an arbitrary value for the total number of messages. Let's choose 90 messages. Then, we have:

4y + x = 90

x = 90 - 4y.

Substituting z = 3y into x = 90 - 4y, we get:

3y = 90 - 4y

7y = 90

y = 90/7 = 15.

Plugging y = 15 into x = 90 - 4y, we get:

x = 90 - 4 * 15 = 30.

Therefore, Tammy sent 30 messages, Felipe sent 15 messages, and David sent 45 messages.

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Answer:

34.98 yds²

Step-by-step explanation:

To find surface area, we add together the area of each side. We have six sides, but there are three sets of identical sides, so it's easier to calculate.

We begin with the sides with dimensions 2.40 and 2.50. Multiply these together.

2.40 · 2.50 = 6

Since there are two of these sides, we can already say that the combined area of them is 12. So, we start the equation with 12.

Next, the two sides with dimensions 2.34 and 2.50. Multiply these together as well, to get 5.85. Multiply this by two to find the area of both sides, 11.7.

Add to our equation, for 12 + 11.7.

For the final two sides, we have the dimensions 2.34 and 2.40. Multiply to get 5.64. Multiply this again by two to find the area of both sides. We get 11.28. Add this to the equation as well, for 12 + 11.7 + 11.28= 34.98.

The answer is 34.98 yds². Good luck :)

Answer:

(0,2)

(1,-3)

(2,-8)

The solutions to the triangle are given as follows:

We consider a triangle with side lengths and angles related as follows:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle A is given as follows:

m < A + 98 + 37 = 180

m < A = 180 - 135

m < A = 45º.

Hence the relations from the law of sines are given as follows:

sin(45º)/18 = sin(98º)/b = sin(37º)/c.

Hence the length b is given as follows:

sin(45º)/18 = sin(98º)/b

b = 18 x sine of 98 degrees/sine of 45 degrees

b = 25.2.

The length c is given as follows:

sin(45º)/18 = sin(37º)/c.

c = 18 x sine of 37 degrees/sine of 45 degrees

c = 15.3.

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Answer:

$100

Step-by-step explanation:

solution:

commission = 12.5% of $800

= $100

Answer:

x > 10

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

ok so how many times does 10 go into 90

1.10

2.20

3.30

4.40

5.50

6.60

7.70

8.80

9.90

9 times so

9

Hope This Helps!!!

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ÷)

Answer:

1

Step-by-step explanation:

Answer:

1).  (x - 4 = 13)

2).  (r + 17 = 51)

3). (7/9x =28)

4). (2/3x = 2)

5). { 3(x-2) = -9 }

6). (x -1.75 = 8.85)

7). Natalie buys organic almonds priced at $77 from the grocery store. How much did

she pay the cashier, if she received $23 in change?

Step-by-step explanation:

1. add 4 on both sides and it will be x=17

2. subtract 17 on both sides and it will be x= 34

3. multiply 9/7 on both sides and it will be x= 257/7 then you divide 257 by 7 then the final answer will be x= 36

4. multiply 3/2 on both sides and it will be x=6/2 then you divide 6 from 2 and the finial answer will be x= 3

5. you will distribute 3 into x and 2 and you will be 3x-6=-9 then you will add 6 on both sides so you will get 3x=3 and then divide 3 on both side so you will get x=1

6. add 1.75 on both sides so x= 10.6

7. the equation will be 23 +x = 77 so first you will subtract 23 on both sides and x will equal 54 so Natalie paid $54

Answer:

i'm taking that test rn

Step-by-step explanation:

Answer:

Thx for free points. remember me? actually answer questions.

Answer:

1/5 or 0.2

Step-by-step explanation:

(-3- -2) / (-4- 1)

-1/-5

Answer:

below

Step-by-step explanation:

1. 1 over 8

2. 4 over 1

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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Answer:a

Step-by-step explanation:

Equivalent expressions are expressions with equal values

The decimal equivalent to 120% is 1.20

The percentage is given as:

n = 120%

Express as fraction

\(n = \frac{120}{100}\)

Divide

n =1.20

Hence, the decimal equivalent to 120% is 1.20

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Answer:

A is (10,0)

B is (3, 3).

Step-by-step explanation:

First we calculate the coordinates of the point A.

Here, y = 0 so we have:

7(0) - 3x + 30 = 0

-3x + 30 = 0

x = -30/-3 = 10.

So A has coordinates (10,0).

Next we find the coordinates of the points where the line passes through the y axis. Here x = 0:

7x - 3(0) = 30

x = 30/7.

So the point is (0, 30/7).

Let the point B have coordinates (x1, y1)  

Now x1 = y1 (given).

If we draw a line from B perpendicular to the x axis ( its length will be = y1) then we have 2 similar triangles.

So  as corresponding sides are in the same ratio:

y1/ (30/7) = (10-x1) / 10  

But as x1 = y1:

x1/ (30/7) = (10-x1) / 10  

7 x1 / 30 = (10-x1) / 10

70 x1 = 30(10 - x1)

70x1 = 300 - 30 x1

100 x1 =  300

x1 = 3

So the coordinates of B are (3,3)

Checking the solution to the equation:

LHS = 3 / 30/7  = 3*7 / 30 = 21/30 = 7/10.

RHS = (10 -3 ) / 10 = 7/10.

Answer:

The Second Number is 90.

Step-by-step explanation:

P.S Can I have brainliest?

The mode will be = 5.2

What is mode?

A set of data values' mode is the value that appears the most frequently. The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable.

Consider the number of missed working days during a certain month of 5 employees of a company, 1,1,2,4,7

Mean age of the given data set will be its arithmetical average. Divide the sum of number of missed working days by 5. That is,

Mean number of days missed = 1+1+2+4+7/5

=15/5

=3days

hence mean = 3 days

Consider the formula for the variance for data set

σ² = ∑(X-µ)²/N

Compute the variance of given data set as follows

= 26/5

=5.2

Hence the variance is 5.2

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The computation is that the width is 21.5 feet and the height is 12.5.

Let the height = h

Let the width = (3 × h) - 16 = 3h - 16

Therefore, the dimensions will be:

h + 3h - 16 = 34

4h = 34 + 16

4h = 50

Divide

h = 50/4

h = 12.5

Therefore width = 3h - 16 = 3(12.5) - 16

= 37.5 - 16

= 21.5

The width is 21.5 feet and the height is 12.5.

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Answer:

Billy has a shirt called: T-The-T. He loves it, it's size 4. One day, he grows a LOT, and he wants to multiply the shirt's size by 3/8.

Answer:

B. 20 feet

Step-by-step explanation:

If the triangles are similar that means the ratio of the sides of the triangles are the same.

Sense the left side of bigger triangle is 4 times bigger than the bottom side of the triangle, then the left side of the smaller triangle is 4 times bigger than the bottom side.

5×4=20

Answer:

neither, neither, terminating, repeating

By finding the average rate of change, we can see that:

a) The cost decreases.

b) The cost increases.

To check that, we need to find the average rate of change on the interval.

Remember that for function f(x) on an interval (a, b), the average rate of change is:

R = (f(b) - f(a))/(b - a)

Here the cost function is:

c(n) = 0.25*n² - 10n + 800

a) In the interval [10, 15] the average rate of change is given by:

R = (c(15) - c(10)/(15 - 10)

Where:

c(15) = 0.25*15^2 - 10*15 + 800 = 706.25

c(10) = 0.25*10^2 - 10*10 + 800 = 725

Then the average rate of change is:

R = (706.25 - 725)/(15 - 10) = -3.75

This means that between 10 and 15 light fixtures, the cost is decreasing.

b) Now we have the interval [20, 25], so let's do the same ting:

c(20) = 0.25*20^2 - 10*20 + 800 = 700

c(25) = 0.25*25^2  - 10*25 + 800 = 706.25

Here the average rate of change is:

R = (706.25 - 700)/(25 - 20) = 1.25

It is positive, which means that the cost is increasing.

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The value of  Q(x) =   x² - 1  

R(x) = 4

What is Long Division?

Long division is a common division procedure in mathematics that may be easily performed manually and is appropriate for dividing multi-digit Hindu-Arabic numbers. It simplifies a division problem into several shorter stages.

By long Division method:

                        x² - 1            

                     _______________________________

         (3x - 4) | 3x³ - 4x² - 3x

                       3x³ - 4x²

                       _________________

                            0 - 0   - 3x      

                                       - 3x + 4  

                                ___________________

                                          0  + 4

Q(x) =   x² - 1  

R(x) = 4

Hence, (3x³-4x²-3x) = (3x - 4)(x² - 1  ) + 4

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Answer:

4 weeks

Step-by-step explanation:

15 x 8 = 120, so Troy bikes 120 miles each day

3360/120 = 28 days or 4 weeks

Answer:

4 weeks

Step-by-step explanation:

3360/(15*8)=28 days. This means it is the total miles divided by how many miles Troy does in one day, which gives the number of days to complete.

Convert days to weeks. 28 days= 4 weeks. This is just dividing the days by seven in order to get the total weeks.

Hope this helped. :-)

1. True  2. True  3. True   4. False

1. Split gateways must have exactly two incoming and at least one outgoing sequence flows: True.

Split gateways, also known as XOR gateways, are used to create exclusive decision points in a process flow. They require exactly two incoming sequence flows, representing the different paths leading to the decision point. Additionally, there must be at least one outgoing sequence flow, indicating the possible outcomes of the decision.

This ensures that the process flow can continue along one of the paths based on the conditions specified in the gateway.

2. Intermediate events must have at least one incoming and one outgoing sequence flow:  True.

Intermediate events occur within the flow of a process and can trigger specific actions or conditions. They must have at least one incoming sequence flow, indicating the event's dependency on a preceding activity or event. Similarly, they must have at least one outgoing sequence flow, showing the subsequent flow of the process after the event occurs.

This ensures that the intermediate event has a clear cause and effect relationship with the surrounding activities.

3. A message flow must connect one pool with a different pool:  True.

Message flows represent the exchange of information between pools in a BPMN (Business Process Model and Notation) diagram. Pools typically represent different participants or organizations involved in a process. A message flow connects an activity or message event of one pool to an activity or message event of a different pool, indicating communication or data exchange between them.

This ensures that the process flow accurately represents the interaction between various participants.

4. Only intermediate catching boundary events can be attached to an activity's border: False.

Both intermediate catching and throwing boundary events can be attached to an activity's border. Intermediate catching boundary events are triggered when certain conditions are met during the execution of the activity. They interrupt the normal flow and allow for additional actions to be performed.

On the other hand, intermediate throwing boundary events initiate an external interrupt and can be used to signal an error or exception. Both types of boundary events can enhance the flexibility and exception handling capabilities of an activity.

In summary, the true statements are:
- Split gateways must have exactly two incoming and at least one outgoing sequence flows.
- Intermediate events must have at least one incoming and one outgoing sequence flow.
- A message flow must connect one pool with a different pool.

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The numbers ordered from least to greatest are 3.6, 3.621, 3.63, 3.702, 3.73, 3.785

The numbers are written in decimals. A decimal is a standard method used to write non-integers. A decimal is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 3.63.

In order to write decimals, from the least to the greatest, if the unit digit and tenth digit are the same, look at the hundredth digit, if the hundredth digit. Order the numbers on the basis of its hundredth digit. Based on this explanation, in the digits 3.6,  3.621, 3.63, 3.6 is the smallest and 3.63 is the largest.

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Answer:

\(\frac{x+20}{x+4}\)

Step-by-step explanation:

Can't cancel out terms like that

need to factor out the top and bottom

\(\frac{x^{2} +16x-80}{x^{2} -16}\) = \(\frac{(x+20)(x-4)}{(x-4)(x+4)}\)   now cancel out the (x-4) from the top and bottom

= \(\frac{x+20}{x+4}\)

Answer & Explanation:

Error: individual terms in an equation in a fraction cannot be directly canceled out.

Correction:

the easy way (solve the quadratic equation in the numerator and complete the square in the denominator):

(x^2 + 16x - 80) / (x^2 - 16)

(x+20)(x-4) / (x+4)(x-4)

x+20 / x+4

the complicated way (manipulate the exponents and common factors):

(x^2 + 16x - 80) / (x^2 - 16)

(x^2 - 4x + 20x - 80) / x^2 - 2^4

x(x^2-1 - 2^2)+4*5(x - 2^4-2) / (x - 2^2)(x + 2^2)

x(x-4)+20(x-4) / (x-4)(x+4)

x(x-4)+(2^2 (5))(x-4) / (x-4)(x+4)

(x-4)(x + 2^2 (5)) / (x-4)(x+4)

(x-4)(x+20) / (x-4)(x+4)

x+20 / x+4