find the value of x and the measure of angle MNQ

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.

Answer:

1. Using Backwards Method, we get,

We have the inequality 2n+5<13.

So, we subtract both the sides by 5,

i.e. 2n+5-5<13-5

i.e. 2n < 8

Now, divide both sides by 2, we get,

[tex]\frac{2n}{2} <\frac{8}{2}[/tex]

i.e. n < 4.

So, using the Backwards method, we get the solution is n<4.

2. Now, we use the Algebraic method,

We have, 2n+5<13

Take 5 to the right side of the inequality,

i.e. 2n<13-5

i.e. 2n < 8

Now, take the 2 on the right side of the inequality.

i.e. [tex]n<\frac{8}{2}[/tex]

i.e. n < 4.

So, again using the Algebraic Method, we get that the solution is n<4.

Answer

Find out the how much of each metal is needed to make 3.6 kg of this alloy .

To proof

As given

An alloy consists of nickel, zinc, and copper in the ratio 2:7:9 .

This shows that an alloy contains 18 parts and assume one part of alloy be u .

Thus

An alloy consists of nickel = 2u

An alloy consists of zinc = 7u

An alloy consists of copper = 9u

As given

Total weight of alloy = 3.6 kg

Thus equation becomes

2u + 7u + 9u = 3.6

18u = 3.6

[tex]u = \frac{3.6}{18}[/tex]

u = 0.2 kg

An alloy consists of nickel = 2 × 0.2

                                           = 0.4 kg

An alloy consists of zinc = 7 × 0.2

                                        = 1.4 kg

An alloy consists of copper = 9 × 0.2

                                             = 1.8 kg

Hence proved

To make 3.6 kg of alloy in the given ratio, 400 grams of nickel, 1400 grams of zinc and 1800 grams of copper are required.

The question is asking how much of each metal, namely nickel, zinc, and copper, is needed to make 3.6 kg of an alloy with a ratio 2:7:9. To solve this, first, we have to understand that the ratio represents relative amounts of each metal, not their exact weights. The entire alloy is made up of 2 parts nickel, 7 parts zinc, and 9 parts copper - a total of 18 parts. We can find the weight equivalent to one part by dividing the total weight of the alloy - 3.6 kg or 3600 grams - by 18. This gives us 200 grams as the weight of one part. To find the weight of each metal needed, we multiply the weight of one part by the number of parts in the ratio: nickel is 2 * 200 = 400 grams, zinc is 7 * 200 = 1400 grams, and copper is 9 * 200 = 1800 grams.

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Option C) is the correct statement as the Theoretical Probability of the coin landing on tails is 1/2

Theoretical probability is the ratio of favorable outcomes to the total number of outcomes.

Experimental probability or empirical probability is based on a particular experiment using the same formula.

Experimental probability of getting heads

= Frequency of heads/Total observations

= 35/100 = 7/20

Experimental probability of getting tails

= Frequency of tails/Total observations

= 65/100 = 13/20

The theoretical probability of getting a heads

= Favorable outcomes of getting heads/Total possible outcomes

= 1/2

The theoretical probability of getting a tails

= Favorable outcomes of getting tails/Total possible outcomes

= 1/2

When we cross-check with the options,

A) Incorrect, as the Theoretical Probability of the coin landing on heads = 1/2

B) Incorrect, as the Experimental Probability of the coin landing on tails = 13/20

C) Correct, as the Theoretical Probability of the coin landing on tails = 1/2

D) Incorrect, as the Experimental Probability of the coin landing on heads = 7/20

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Answer:

The cube root of 9

Step-by-step explanation:

The required inequality is -6n - 5 ≥ 8. Option (C) is correct.

Inequality shows relation between two expression which are not equal to each others.

Given that,

When 5 is subtracted from the product of number n and -6 is at least 8.

The product of number n and - 6  = -6n

Subtract 5 from product of number n and -6 = -6n - 5

To write the inequality that shows that 5 less than -6n is at least 8,

Implies that, -6n - 5 can be grater than or equal to 8.

The inequality can be expressed as,

-6n - 5 ≥ 8

Hence, option (C) is correct.

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