\sqrt{6} + 3 \sqrt{6}

Answer:

Collinear, coplanar, and between the points

Step-by-step explanation:

Collinear means that the points are in the same line.

Coplanar means that the points are in the same plane.

Between the points is used when three points are in the same line an you want tro express that one of them is between the others.

So those three relationships can apply for the three points.

noncollinear not apply because it means that the points don't lie in a line.

It would take 3.625 gallons of gasoline to fill a 14.5-gallon tank that is already 3/4 full.

The question asks how many gallons of gasoline are needed to fill a 14.5-gallon tank that is already 3/4 full. To find the amount needed to fill the tank, we first determine how much gasoline is currently in the tank by multiplying 14.5 gallons by 3/4:

14.5 gallons × 3/4 = 10.875 gallons

This means that there are 10.875 gallons of gasoline in the tank at the moment. To find out how much more gasoline is needed to fill the tank, we subtract this amount from the tank's total capacity:

14.5 gallons - 10.875 gallons = 3.625 gallons

Therefore, it would take 3.625 gallons of gasoline to fill the tank.

To calculate an increase, multiply the original value by the percentage increase. For simple interest, use the formula Interest = Principal * Rate * Time. Percentage increase in mass can be found with the formula: [(Final mass - Initial mass) / Initial mass] * 100%. These methods result in a new train fare of £24.21, a bank balance after 5 years of £472, and a 25% increase in the puppy's mass.

1. To work out the new fare, we first need to calculate how much the fare has increased by. 2.8% of £23.55 is found by multiplying 23.55 by 0.028, which comes out to £0.66 (rounded to the nearest penny). Adding this increase to the original fare gives us a new fare of £24.21.

2. The simple interest can be calculated using the formula Interest = Principal * Rate * Time. In this case, Heidi's investment of £400 (the principal) is earning 3.6% (the rate) in interest every year for 5 years (the time). So, the interest Heidi earns equals £400 * 3.6% * 5 = £72. Adding this to the original amount gives us £472.

3. The percentage increase in the puppy's mass is calculated as follows: [(2.25 kg - 1.8 kg) / 1.8 kg] * 100%. So, the mass has increased by 25%.

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Final answer:

The weight of 11 candy bars is calculated by multiplying the weight of one candy bar, which is 3 ounces, by 11. The total weight for 11 candies is equal to 33 ounces.

Explanation:

If one candy bar weighs 3 ounces, the weight of 11 candy bars can be found by multiplying the weight of one candy bar by the number of candy bars. The calculation would be as follows:

Multiply the weight of one candy bar by the number of candy bars: 3 ounces × 11 = 33 ounces.

Therefore, the weight of 11 candy bars is equal to 33 ounces.

Step-by-step explanation:

Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe  and V be the volume of swimming pool.

[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]

If both pipes are combined it takes 213 hours, that is

              [tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]

Now we need to find how much time it takes to fill the pool by large pipe,

That is

               [tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]

By large pipe only it will take 319.5 hours to fill the pool.          

1. The measure of angle A is [tex]\(22^\circ\).[/tex]

2. The measure of angle B is[tex]\(68^\circ\).[/tex]

To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:

[m_A + m_B = 90]

Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:

3x - 8 + 5x + 10 = 9

Combine like terms:

8x + 2 = 90

Subtract 2 from both sides:

8x = 88

Divide by 8:

x = 11

Now that we know the value of (x), we can find the measures of angles A and B:

[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]

[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]

Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:

25 + 65 = 90

So, angles A and B satisfy the condition of being complementary.

"The correct expression to show the total number of empty spaces in the bike racks is [tex]\( 4 \times 15 - 16 \).[/tex]

To arrive at this expression, we start by calculating the total capacity of all the bike racks combined. Since there are 4 bike racks and each can hold 15 bikes, the total capacity is [tex]\( 4 \times 15 \).[/tex] This gives us the maximum number of bikes that can be parked in all the racks.

Next, we subtract the number of bikes that are currently parked in the racks from the total capacity. There are 16 bikes parked. Therefore, the expression to find the number of empty spaces is:

[tex]\[ \text{Total capacity} - \text{Number of bikes parked} \][/tex]

Substituting the given numbers into the expression, we get:

[tex]\[ 4 \times 15 - 16 \][/tex]

This expression represents the total number of empty spaces in the bike racks. When evaluated, it will give us the number of spaces available for additional bikes to be parked."

It will take Kristin 24 minutes to catch up to the truck. She will travel a distance of 20 miles in that time.

To calculate how long it will take for Kristin to catch up to the truck, we can use the equation: time = distance / speed. Since Kristin is 20 miles behind the truck, she will need to cover a distance of 20 miles to catch up to the truck. Assuming she drives at a constant speed, we can use her speed as the truck's speed since she needs to match it to catch up.

Time to catch up = 20 miles / 50 miles per hour = 0.4 hours = 24 minutes.

In that time, Kristin will travel the same distance as the truck. So, she will go 20 miles in 24 minutes.

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Answer:

Step-by-step explanation:

Answer:

Deanne

Step-by-step explanation:

Deanne is a consumer

Answer:

The correct option is C.

Step-by-step explanation:

The given table represent the number of contestants in each round of the competition.

The average rate of change of f(x) from x = 3 to x = 5.

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

[tex]m=\frac{f(5)-f(3)}{5-3}[/tex]

[tex]m=\frac{4-16}{2}[/tex]

[tex]m=\frac{-12}{2}[/tex]

[tex]m=-6[/tex]

The average rate of change of f(x) from x = 3 to x = 5 is -6, it represents the average rate at which the number of contestants decreased from the third round to the fifth round.

Therefore option C is correct.

round miles up to 84

round gallons down to 2

 and divide

84 /2 = 42 miles per gallon ( estimate)