Please help with question, thanks

To express ln x + a ln y - b ln z as a single logarithm, use the properties of logarithms.

To express ln x + a ln y - b ln z as a single logarithm, we will use the properties of logarithms. The key properties we will use are:

Using these properties, we can simplify the expression:

ln x + a ln y - b ln z = ln x + ln(y^a) - ln(z^b)= ln (x(y^a)/(z^b))

So, the given quantity can be expressed as a single logarithm: ln (x(y^a)/(z^b))

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Answer:

630 cm 3 is the answer to the question

Sadie will make 3 gallons of punch.

First, let's convert all the measurements to the same unit, such as gallons.

1 gallon = 4 quarts

1 gallon = 8 pints

1 gallon = 16 cups

Now, let's convert each ingredient:

1. Lemon-lime juice: 8 quarts = 8/4 = 2 gallons

2. Vanilla ice cream: 4 pints = 4/8 = 0.5 gallons

3. Orange juice: 8 cups = 8/16 = 0.5 gallons

Now, let's sum up the amounts of each ingredient:

2 gallons (lemon-lime juice) + 0.5 gallons (vanilla ice cream) + 0.5 gallons (orange juice) = 3 gallons

Complete question: Using 8 quarts lemon-lime juice , 4 pints vanilla ice cream , 8 cups orange juice .How many gallons of punch will Sadie make?

Answer: 25

Step-by-step explanation:

Pythagorean theorem

c=√a²±b²

So it was 7=A

And it was 24=b

solving that it gives us 25

This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.

Hope this helps-A

The maximum width of the slot is 25cm (Option A).

To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.

Given:

- The length of the rectangle (one side) = 24 cm

- The height of the rectangle (other side) = 7 cm

The formula for the diagonal [tex]\( d \)[/tex] is:

[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]

Substituting the given values:

[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]

[tex]\[ d = \sqrt{576 + 49} \][/tex]

[tex]\[ d = \sqrt{625} \][/tex]

[tex]\[ d = 25 \, \text{cm} \][/tex]

So, the maximum width of the mail slot is 25cm.

Full Question:

Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.

The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.

What is the maximum width of the mail slot?

A) 25

B) 31

C) 22

D) 20

Answer:

there is no solution

Step-by-step explanation:

The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.

To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.

The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.

The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.

The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.

The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.

Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.

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Final answer:

Michelle's stamp collection consists of 60% U.S. stamps, determined by solving equations based on the given information that U.S. and Mexican stamps make up 80% of her collection and there are three times as many U.S. stamps as Mexican stamps.

Explanation:

The student asked what percent of Michelle's stamp collection is made up of U.S. stamps if 80% are U.S. and Mexican stamps and there are 3 times as many U.S. stamps as Mexican stamps. To solve this, let's call the percentage of U.S. stamps 'U' and the percentage of Mexican stamps 'M'. According to the given information, U + M = 80%, and U = 3M.

We substitute the second expression into the first to get 3M + M = 80%, which simplifies to 4M = 80%. Dividing both sides by 4 gives M = 20%. As the number of U.S. stamps is three times the number of Mexican stamps, we calculate U as 3 × 20% = 60%. So, the percentage of U.S. stamps in Michelle's collection is 60%.

Answer:

D.  x^2 = -16y

Step-by-step explanation:

got it right on edge

Rex uses 2.25 gallons of paint on the shed, which is [tex]\( \frac{3}{4} \)[/tex] of the 3 gallons of paint he uses on the garage.

To find out how much paint Rex uses on the shed, we need to calculate [tex]\( \frac{3}{4} \)[/tex] of the amount of paint he uses on the garage.

Rex uses 3 gallons of paint on the garage.

Therefore, the amount of paint he uses on the shed is:

Paint used on the shed = [tex]\frac{3}{4} \times 3[/tex]

Calculating this:

Paint used on the shed = [tex]\frac{3 \times 3}{4}[/tex]

= [tex]\frac{9}{4}[/tex]

= 2.25

So, Rex uses 2.25 gallons of paint on the shed.

Answer:

It is q i  think

Step-by-step explanation: