Two friends get frozen yoghurt. The rate the topping is 4:3. If one of the friends has 4.5 oz of topping in their bowl, which of the following is the amount of yoghurt in their dessert?

Yoghurt : toppings=4:3

Yoghurt: 4.5 oz =4:3

We convert the given ratio into a proportion equation as below

Multiply both sides by 4.5 oz

Since the screen sizes are proportional, we can set up a proportion based on the diagonal lengths of the screens.

Let x be the length of the vehicle on the 50-inch screen. The proportion based on the screen sizes is:

=

Now, solve for x:

x = = ≈14.06

Rounding to the nearest inch, the vehicle will appear about 14 inches long on the 50-inch screen.

In a negatively-correlated variables, a change in one variable result in opposite change in the other variable. In other words, an increase in on variable results in a decrease in the other.

Now let’s analyze the given scenarios:

As elevation increases, temperature decreases is a NEGATIVE CORRELATION

As elevation increases, temperature increases is a POSITIVE CORRELATION

As elevation decreases, temperature remains the same this is NO-CORRELATION

As elevation decreases, temperature decreases is a POSITIVE CORRELATION

To solve this problem, we need to find the mean, mode and median of the above data set.

From the data set, the mode of the data is 2 and 8. They are the most occurring elements in the data set.

Mean of data is total divided by number of elements

Total=1+ 1 + 2+ 2+ 2+ 2+ 3 +3+ 7+ 7+8+8+ 8+ 8+ 9+9=80

Number of elements=16

Mean=80/16=5

Median will fall in between the (N/2)th and (N/2+1)th position

(N/2)th =16/2 =8th position and (16/2+1)th =9th position

Since the data is arranged in ascending order as below

1, 1, 2, 2, 2, 2, 3, 3, 7, 7, 8, 8, 8, 8, 9, 9

Element in 8th position = 3

Element in 9th position =7

So median average of the two elements=(3+7)/2=5

Now the data could be presents as follows in the distribution curve

This is because the data set has two modes, meaning the data is bimodal.

To find the area of the largest circle that fits in the rectangle, we need to determine the area of a circle with a diameter of 8 cm or less to fit on the rectangle with the given measurements as illustrated below.

​​​​​​​

Area of circle= πr2

Radius of circle, r=8cm/2=4cm

Then, area of the largest circle is:

Area of circle= π*4 cm *4 cm =16π cm2

In direct proportion relation we utilize the relationship as:

Variable∝Variable 2

Thus from the given case,

Force∝stretch

We introduce a constant term, K to remove the sign of proportionality as

Force=K* stretch

Let’s find the value of K, using Force=132 N and stretch of 0.07 m

132 N=K*0.07 m

K=132 N/0.07 m=1885.7 N/m

Now substitute this value of K in the following equation

Force=1885.7 N/m * stretch

For a stretch of 0.1 m, the force needed is

Force=1885.7 N/m * 0.1 m=188.57 N=188.6 N

Rounded to the nearest dollar, the original price of the recliner is approximately $451.

Here are the calculations for the gumballs:

• Total Gumballs: 120
• Red Gumballs: 20% of 120 = 24
• Orange Gumballs: 30% of 120 = 36
• Yellow Gumballs: 5% of 120 = 6
• Green Gumballs: 10% of 120 = 12
• Blue Gumballs: 120−(24+36+6+12) =42

Difference

The difference between the number of blue gumballs and yellow gumballs is: 42 − 6=36

The constant of proportionality is the distance traveled divided by gallons of gas consumed

Constant of proportionality=386.4 miles/14 gallons= 27.6 miles per gallon.

Use the order of operations to solve the given equation. The acronym PEDMAS will help us to solve the given problem.

P- Parenthesis

E-Exponents

D-Divide

M-Multiply

A-Add

S-Subtract

From the given equation start with solving

12 ÷3*4-1+23

Next, carry out division 12÷3=4

4*4-1+23

Multiply is 4*4=16

16-1+23

Add or subtract can be conducted in any order. From left to right, we subtract followed by addition

Subtract 16-1=15

15+23

The last step is to add 15+23

15+23=38

Thus, the answer to the given equation is 38.