At a recent Sing Thing, it was found that together, Anne and Bob weigh 180 kg, Carl and Dee weigh 210kg, and Ann and Carl weigh 220kg. Together, Bob and Dee weigh,

The equivalent expression is a+ 2b.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

2(a+2b)-a-2b

Now, solving the expression we get

= 2(a + 2b) - a - 2b

= 2a + 4b - a -2b

= 2a - a + 4b - 2b

= a + 2b

Hence, the equivalent expression is a+ 2b.

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The first error that Carlos made was B) Step 2 should have been 14(40) + 14(9).

We can analyze Carlos's work and the suggested steps to determine the first error:

Analysis of Errors:

Step 1:

49 was split into 40+9, which is correct.

Step 2:

This step should distribute 14 to both 40 and 9 and not only to 40.

Correct version:

14×40+14×9.

Step 3:

Carlos only computed 14×40 and ignored multiplying 14×9.

The correct version calculates both parts as

14×40 = 560 and 14×9 = 126.

Step 4:

The addition of 560+9 is wrong since it doesn't account for the correct 126 from 14×9.

Correct version should add 560+126 to get 686.

Thus, the first error Carlos made was in Step 2, where he incorrectly distributed 14 only to 40 and not to 9, failing to apply the distributive property.

Complete Question:

Carlos is using the distributive property to evaluate the expression 14 (49) by using friendlier numbers. His work is shown below. Carlos’s Work 14 (49)

Step 1: 14 (40 + 9)

Step 2: 14 (40) + 9

Step 3: 560 + 9

Step 4: 569

What was the first error that Carlos made?

A) Step 1 should have been 14(7 + 7).

B) Step 2 should have been 14(40) + 14(9).

C) Step 3 should have been 23(40).

D) Step 4 should have been 5,040.

To convert from pounds to tons, divide the number of pounds by 2,000. A Class 2 truck, which weighs between 6,000 and 10,000 pounds, would weigh between 3 and 5 tons.

To convert the weight range of a Class 2 truck from pounds to tons, we must know the unit equivalence that 2,000 pounds is equal to 1 ton. Since we're converting from a smaller unit (pounds) to a larger unit (tons), we need to divide.

The lower end of the range:

6,000 pounds / 2,000 pounds per ton = 3 tons

The upper end of the range:

10,000 pounds / 2,000 pounds per ton = 5 tons

Therefore, a Class 2 truck weighs between 3 and 5 tons.

Answer:

7.7

Step-by-step explanation:

Its 7.7 kilograms

The true statement are as follows:

Here's a breakdown of why each statement is true or false:

True:

If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. As the painting time increases, the hourly rate becomes a bigger factor, and Splash of Color's lower rate outweighs Interior Designs USA's initial fee advantage.

If it takes 3 hours to paint the rooms, both companies will charge the same amount. Both companies will charge 3 hours of labor at their respective rates: $35/hour * 3 = $105 for Interior Designs USA and $55/hour * 3 = $165 for Splash of Color.

False:

If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. Interior Designs USA will cost $60 + $35/hour * 7 = $315, while Splash of Color will cost $55/hour * 7 = $385.

Splash of Color will always charge the least. This is not true because Interior Designs USA can be cheaper for smaller jobs due to their lack of an initial fee (e.g., 1 hour painting time).

If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. Splash of Color will cost $55/hour * 10 = $550, while Interior Designs USA will cost $60 + $35/hour * 10 = $410. The difference is actually $140, not $200.

Complete question:

Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

The cost of one greeting card Marianne bought is $9.45/x.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Marianne spends $9.45 on greeting cards, and let she bought 'x' numbers of cards.

Therefore, As the cost of each greeting card is the same, The cost of one card can be obtained by dividing the total cost by the total number of cards which is,

= $(9.45/x).

So, The cost of one greeting card is $(9.45/x).

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Answer:

Each shrub is $9.

Step-by-step explanation:

You are looking for the price of the shrub plants. Since you know that the plants' price with the soil's price totals the purchase at $53.50, your equation should look like this:

[tex]4p + 17.50 = 53.50[/tex]

After that, use the order of operations to solve the price of the shrubs.

[tex]4p + 17.50 = 53.50 \\4p + 17.50-17.50 = 53.50-17.50\\4p = 36\\4p/4 = 36/4\\p=9[/tex]

Answer:

Step-by-step explanation:

The picture that shows the needed information is attached.

According to the graph, the distance showed between Gendet and Montrose is 1.5cm with a scale of 1 centimeter = 16 kilometers.

This scale means that each centimeter on the paper represents 16 kilometers of the real distance. So, what we need to do is just multiply the 1.5 cm by 16 km, because that's the scale:

[tex]1.5(16)=24[/tex]

Therefore, the actual distance is 24 kilometers.

The expressions rewritten using the distributive property are:

1. -12x + 24

2. 4x - 24y

3. 30 - 6q

4. [tex]\(\frac{c}{2} - 4\)[/tex]

5. -15 + 3b

6. -7D - 14

To rewrite each expression using the distributive property:

1. 3(-4x + 8):

  [tex]\[3 \cdot (-4x) + 3 \cdot 8\][/tex]

  -12x + 24

2. 4(x - 6y):

  [tex]\[4 \cdot x - 4 \cdot 6y\][/tex]

  4x - 24y

3. 6(5 - q):

  [tex]\[6 \cdot 5 - 6 \cdot q\][/tex]

  30 - 6q

4. [tex]\(\frac{1}{2}(c - 8)\)[/tex]:

  [tex]\[\frac{1}{2} \cdot c - \frac{1}{2} \cdot 8\\ \[\frac{c}{2} - 4\][/tex]

5. -3(5 - b):

  [tex]\[-3 \cdot 5 + 3 \cdot b\][/tex]

  -15 + 3b

6. (D + 2)(-7):

  [tex]\[D \cdot (-7) + 2 \cdot (-7)\][/tex]

  -7D - 14

So, the expressions rewritten using the distributive property are:

1. -12x + 24

2. 4x - 24y

3. 30 - 6q

4. [tex]\(\frac{c}{2} - 4\)[/tex]

5. -15 + 3b

6. -7D - 14

To find the value of x in the equation x + 4/5 = 11, you subtract 4/5 from both sides and then simplify the resulting fraction, giving you x = 10.2.

To solve the equation x +  {4}/{5} = 11, we need to isolate the variable x. First, subtract  rac{4}{5} from both sides of the equation:

x +  {4}/{5} -  {4}/{5} = 11 -  {4}/{5}

This simplifies to:

x = 11 -  {4}/{5}

To subtract the fraction from 11, which is a whole number, we can write 11 as a fraction with the same denominator:

x =  {55}/{5} -  {4}/{5}

Now, subtract the numerators:

x =  {55 - 4}/{5}

x =  {51}/{5}

Finally, divide 51 by 5:

x = 10.2

Answer:

$10.

Step-by-step explanation:

We have been given a function [tex]y=10.00x+35[/tex], where  y represents the cost of cabin lodging per occupant and x represents the number of occupants.

Since slope of a line is also known as unit rate, so the cost increase for every occupant will be equal to the slope of line.

We can see from our given expression that 10.00x represents the slope of line, so the cost increase for every occupant is $10.

Answer:

Step-by-step explanation: