A girl and a dog are playing tug of war with a piece of rope. The girl pulls on the rope with a force of 165 newtons (N) towards the east, and the dog pulls with a force of 190 N towards the west. What is the net force on the rope?

We use the properties of exponent with the same base to solve for above expression.

Multiplication of exponents with same base, we add the exponents

Division of exponents with same base, we subtract the exponents

Using these two properties, we can solve the expression:

Now we use the following properties:

y0 =1, and, thus

total muffin is equal to the sum of the different muffins sold.

Total muffins=41+27+20=88 muffins

Thus, the bakery sold about 90 muffins.

The whole pie chart represents 100%, which we use together with the given percentages to find the respective different sports. Note that 100% is equal to 500 surveyed students. The, the number of teenagers who prefer:

Soccer

Hockey

Football

Basketball

Other

From the evaluations above, 90 teenagers love soccer, 80 love hockey, 190 teenagers love football, 120 teenagers love basketball, and 20 teenagers love others.

Here we collect like terms together and solve for the unknown value of x.

7x-6=3x-26

Add 6 to both sides of the equation

7x-6+6=3x-26+6

7x=3x-20

Subtract 3x from both sides of the equation

7x-3x=-20

4x=-20

Divide both sides by 4

4x/-4=-20/4

x = -5

The value of x = -5

all products represent 100%. Then, the portion of defect products is:

0.0025 of 100%

‘of’ means multiply

0.0025 *100%=0.25%

The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.

Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week.Histograms are useful for understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.

As you can see below, the Histogram is used to depict a pattern/continuous data. While a bar graph does just fine even with discrete data.

We convert the given weight in pounds to ounces and find total weight. 1 pound=16 ounces, which we interpret as

Or

Use the second option to convert pounds to ounces

Now, we can ounces to ounces as: 48 oz + 5 oz= 53 oz

Therefore, 3 pounds, 5 ounces is equal to 53 oz

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.

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,

from the provided table, the first option represents the amount of gas in gallons while the second column shows the distance in miles. Thus, (6, 144) will denote that the car can 144 miles by consuming 6 gallons of a gas.