All categories

3 years ago

How many 3/4 ounce spoonfuls of sugar are in a 5 1/2 ounce bowl? show work please

Mathematics

1 answer:

klasskru [66]3 years ago

5 0

Answer: $\frac{22}{3}$

Step-by-step explanation: Divide

$5\frac{1}{2}\div \frac{3}{4}$

Step 1: Convert the mixed number to improper fraction

$5 \frac{1}{2} =\frac{11}{2}$

$= \frac{11}{2}\div \frac{3}{4}$

Step 2: Reciprocal

$\frac{11}{2}\times \frac{4}{3}$

Step 3: Divide the common factors

$4 \div 2 = 2\\\\=\frac{11}{1}\times \frac{2}{3}$

Step 4: Multiply

$\frac{11\times \:2}{1\times \:3}\\\\=\frac{22}{3}$

You might be interested in

A certain car rental location charges a daily fee as well as a mileage charge. On one trip a businessman rented a car for the da

nikklg [1K]

Answer:

$x\approx 267\ miles$

Step-by-step explanation:

<u>Linear Modeling</u>

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

$f(x)=mx+b$

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

$c = mx+b$

We must find the values of m and b with the data provided. Substituting the first point:

$79 = 150m+b$

Substituting the second point:

$63.70 = 65m+b$

Both equations form the following system:

$\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.$

Subtracting both equations:

$150m-65m=79-63.70$

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

$85m=15.3$

Solving:

$m=15.3/85=0.18$

From the first equation

$79 = 150m+b$

Solving for b:

$b=79-150m=79-150(0.18) = 52.$

The model for the problem is:

$c=0.18x+52$

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

$100=0.18x+52$

Solve for x:

$0.18x+52=100$

$0.18x=100-52=48$

$x=48/0.18=266.67$

Rounding to the closest integer:

$\boxed{x\approx 267\ miles}$

7 0

3 years ago

Can someone help me with this pls

astraxan [27]

Answer:

3 the rest of his classmate

4 0

3 years ago

Given the radius is 6 inches, what is the area of the circle?

enyata [817]

Answer:

I wasn't sure how you're supposed to answer, so the answers for each scenario are in the explanation!

Step-by-step explanation:

$A=\pi r^{2}$

$A=\pi (6^{2})$

$A=\pi (36)$

From here, there can be a few different answers:

The exact answer is A=36π inches^2.

If you need to round, round this to wherever you need it: A=113.0973355292326... inches^2

If you're using 3.14 for pi, the answer is A=113.04 inches^2.

8 0

3 years ago

Take the following numbers and calculate the mean, median and mode. 75, 65, 70, 70, 55, 40, 55, 70, 65

emmainna [20.7K]

1. mean

To solve for mean, add all the numbers, and divide by the amount of numbers there is.

(75 + 65 + 70 + 70 + 55 + 40 + 55 + 70 + 65)/9 = 565/9 = 62 7/9 (a. 62.8)

2. Median

To solve for median, reorder all numbers from least to greatest, and the middle number is your median.

40, 55, 55, 65, 65, 70, 70 , 70, 75

Middle number is bolded

40, 55, 55, 65, 65, 70, 70, 70, 75

(b. 65)

3. Mode

To solve for mode, find out which number shows up the most.

(c. 70) shows up once more than the next number that has the most (55 & 65, which both have 2)

4 0

4 years ago

Read the following statement: If the sum of two angles is 90°, then the angles are complementary. The hypothesis of the statemen

xeze [42]

Hey there!

It seems your problem is simply trying to rewrite the sentence.

Let's rewrite our sentence, from the phrase after the comma to the phrase before the comma.
Essentially, we are just flipping the sentence structure.

It should be this:
The two angles are complementary if the sum of the two angles are 90 degrees.

Let's take a good look at our answers.

A.) There are two angles.
While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.

B.) The sum of two angles is 90 degrees.
This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.

C.) The angles are complementary.
This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.

D.) Angles are complementary if their sum is 90 degrees.
This is an accurate statement, and provides details to support it's claim, also rewriting the original sentences into one properly. This answer choice is correct.

Your answer is D.)

I hope this helps!

8 0

3 years ago