The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be the correct for the lengths of the other two sides of the triangle? (Note: A2 + B2= C2)

We solve the problem by first finding the amount of gallons needed for the whole trip then find the cost of the gallon.

The car uses 1 gallon to cover 25 miles, which is same as:

Now, in 3000 miles, the car will use how many gallons of gasoline?

A trip of 3000 miles will need 120 gallons. And to find the cost of 120 gallons, we proceed as follows:

The family will spend $199.20 to drive for 3000 miles.

From the given options, we can arrange the numbers from the smallest to the largest as:

-271.906, -193.823, 145.884, 235.971

From the above, it can be noted that -271 is less than -193 while 235 is more than 145.

In this problem, we take the triangle as a right-angled triangle and label it as follows:

From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13.  Mathematically,

But C=13 inches

If we take A=5 inches and B=12 inches, then

Next, we take A=2.5 inches, B=6 inches

Next, we take A=2.5 inches, B=4 inches

6.25+16=169

22.25≠169

Taking A=5 inches and B=8 inches

From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.

A teaspoon can approximately hold 5 mL.

Although the capacity of a teaspoon could be more or less, choice D remains the most correct answer as the other choices have amounts too much for a small teaspoon.

From the given scenario:

Initial charge is $40

Additional charge per circular cloth=$5c

Additional charge per rectangular cloth=$3.50r

Total cost = additional charge per circular rectangular cloths + Initial charge

Total cost, T = 5c + 3.5r + 40

The median temperature can be found by organizing the temperature values from the smallest to the largest value as follows:

98.6, 98.7, 99.0, 99.0,99.2, 99.3, 99.7, 100.0

(for an even set of numbers, Median = frac{(frac{n}{2})th observation + (frac{n}{2} + 1) th observation}{2})

From the data set above, there are 8temperature values. The median is the temperature value in the middle position, which falls between the(frac{n}{2} th)and((frac{n}{2} + 1) th) position. Here N=8and median is found as:

(frac{(frac{n}{2})th + (frac{n}{2} + 1) th}{2} = )(frac{(frac{8}{2})th + (frac{8}{2} + 1) th }{2} = 4.5th position)

The element in the 4.5th position is the average of the 4th and 5th element.

(frac{99.0 + 99.2}{2} = 99.1)

Thus 99.1 is the median temperature.

We are given that 1 teaspoon=4.93 mL, we can interpret it as:

Or

Since we are to find the amount in mL, we look for an option that will cancel teaspoon and remain with mL. The second option is the required conversion, and we proceed as follows:

Therefore, 2.5 teaspoons hold about 12.325 mL.

To find the net force, we choose east direction as positive and west as negative. From this, we can present the tag of war in the diagram below.

So, the force on the dog is -190 N and that of the girl is 165 N.

The net force is the sum of the two forces

The resulting force is negative, meaning it is in the west direction. Thus, the net force is 25 N to the west.

we use the US customary system of units’ equivalent to convert from yards to inches. We know that 1yard=3 ft, and 1 ft =12 inches.

First, convert 2 ¾ into an improper fraction.

Then,

When dividing fractions, the division sign is changed into multiply sign and the first fraction is multiplied by the inverse of the second fraction.

Change division to multiply sign and find invers of 5/8. The inverse of a fraction is inverting the given fraction. The denominator becomes the numerator and the numerator becomes the denominator.