To solve the inequality 4 x < 8, you would divide both sides of the inequality by 4.

Lily sells loose tea for $0. 71 per gram. If one gram is equivalent to 0. 035273 ounces, how much does it cost to buy 0. 45 poun

Dominik [7]

Unit conversion is a way of converting some common units into another. The cost of buying 0.45 pounds of Lily's tea is $144.93.

<h3>What is Units conversion?</h3>

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

As it is given that one gram is equivalent to 0.035273 ounces, while 1 pound is equal to 16 ounces. Therefore, if we convert 0.45 pounds to grams,

Pounds to Ounces

$\rm 1\ pound = 16\ ounces\\\\0.45\ pounds = 0.45 \times 16 = 7.2\ ounces$

Grams to Ounces

$\rm 1\ gram = 0.035273\ ounces\\\\1 ounce=\dfrac{1}{0.035273} = 28.35\ grams\\\\7.2\ ounces = 7.20 \times 28.35 = 204.12\ grams$

Since it is given that the cost of 1 gram of tea is $0.71, therefore, the cost of 204.12 grams of tea can be written as,

$\rm Total\ cost= 204.12 \times \$0.71 = \$144.93$

Hence, the cost of buying 0.45 pounds of Lily's tea is $144.93.

Learn more about Units conversion:

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3 0

2 years ago

Please I’ve attached the question can you help me

Andreyy89

Answer:

1. n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. D. I, II and III.

Step-by-step explanation:

U = {21, 22, 23, ..., 64}

A prime number is a number that can be divided only by 1 and itself.

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B = {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

C = {6, 10, 12, 15, 20, 30, 60}

1. Find n[(A U B) - C]

n(A U B) = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63}

n[(A U B) - C] = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63} - {6, 10, 12, 15, 20, 30, 60}

Since only 30 and 60 are common to n(A U B) and C, we therefore remove them it and have:

n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. Find n[(A - B) U C]

To get n(A - B) we remove all the elements of B in A. Since there are no common elements between A and B, we therefore have:

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

C = {6, 10, 12, 15, 20, 30, 60}

Therefore, we have:

n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. Which of the following is/are true?

I. A ∩ B = A ∩ C

A ∩ B = ∅

A ∩ C = ∅

Therefore, A ∩ B = A ∩ C is true.

II. A - B = A - C

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

A - C = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

Therefore, A - B = A - C is true.

III. A ∩ (B ∪ C) = ∅

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B U C = {6, 10, 12, 15, 20, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

Therefore, A ∩ (B ∪ C) = ∅ is true.

Therefore, the correct option is D i.e. I, II and III are true.

4 0

3 years ago

Write the coordinate of the intercept

Basile [38]

Answer:

m = 2/3

y-intercept: 2

Explanation:

First convert this equation into standard form by distributing the 6y and -4x from the coefficient of 2, and then putting the variables in order.

This equation should be in the form: Ax + By = C (Standard form)

y = -Ax/B + C/B : y = mx + b (Slope intercept form)

2(6y - 4x) = 24 → 12y - 8x = 24

→ -8x + 12y = 24 → -8x = -12y + 24 → 8x = 12y - 24 → 8x - 12y = -24

8x - 12y = -24

| | |

A B C

Once you have standard form, you are ready to convert this into slope intercept by isolating the y completely.

8x - 12y = -24

-8x -8x

(First through the subtraction property of equality, remove 8x from both sides so that -12y is by itself on the left)

-12y = -8x - 24

×-1 ×-1 ×-1

(Through the identity property of negative 1, remove the negative sign from all of the numbers because a negative times a negative is a positive)

12y = 8x + 24

(Lastly, through the division property of equality, divide all sides by 12 because it is the coefficient of y, which will solve for the variable)

8 0

3 years ago

Prince Ivan rides gray wolf and a constant speed from kings castle to the magic apple garden in five hours. on the return trip t

borishaifa [10]

Answer:

The original speed of the grey wolf can be 9 and/or 48 km/hour

Step-by-step explanation:

There are two trips. One to King Castle (KC) to Magic Apple Garden (MAG), and then back (MAG - KC).

First trip: KC - MAG

It takes the same distance as MAG - KC so distance can be D for both.

Then it is stated that it takes 5 hours or 300mins for him to go from KC - MAG, and the speed is constant.

Let x be speed.

So the equation for this is:

D=5x

Second trip: MAG - KC

Here he goes 36 mi at constant speed (x), then picks up his speed by 3 km/hour (x+3).

For Time:

He reaches to KC, 15 mins earlier than KC - MAG, so he reaches there in 4.75 hours or in 275 min.

The problem splits into two as there are two different times, for the two parts of the journey or distance for MAG - KC.

Let T#1 = a, and T#2 = b.

Let D#2 = D-36

The equation for a:

a = 36/x --> This is he is at a constant speed and went for 36mi.

b = (x+3)/D#2

These two equation have to be added as (a+b) = 4.75 --> 4.75 is the total time for MAG - KC.

So the equation is:

36/x + (5x-36)/x+3 = 4.75 --> Knowing (a+b) = 4.75, just put 4.75 as the equal, and add the fractions that equal (a) and (b).

Now Solve:

36/x + (5x-36)/x+3 = 4.75

0.25s^2 + 108 + 5s^2 - 36s = 4.75s*(s+3)

0.25s^2 - 14.25s + 108 = 0

(14.25 +- Square root (203.06 - 108))/0.5

(14.25 +- Square root (95.0625))/0.5

(14.25 +- 9.75)/0.5

Answer:

s = 9, s=48.

Therefore the original speed of the grey wolf can be 9 and/or 48 km/hour.

8 0

3 years ago

22+(-18) find the sum of the answer

Vadim26 [7]

It’s 4 because it’s a positive 22 and the 18 is negative so you do a positive 22 plus a negative 18 and you get 4 as your answer

4 0

4 years ago

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