What is the length of one leg of the triangle

Answer:the number of washes after which 24 ounces will remain in the bottle is:

36 washes.

Step-by-step explanation:

The correct answer is 18.

To find the equation that can be used to determine the number of washes (x) after which 24 ounces of shampoo will remain in the bottle, we need to set up an equation based on the given information.

Given information:

- Initial amount of shampoo in the bottle (I) = 60 ounces

- Amount used per wash (U) = 2 ounces

- Remaining amount after x washes (R) = 24 ounces

[tex]I - (U \times x) = R[/tex]

[tex]60 - (2 \times x) = 24[/tex]

[tex]60 - 24 = 2x[/tex]

[tex]36 = 2x[/tex]

[tex]x = \frac{36}{2}[/tex]

[tex]x = 18[/tex]

Therefore, the equation that can be used to find x is:

[tex]60 - (2 \times x) = 24[/tex]

And the number of washes after which 24 ounces of shampoo will remain in the bottle is 18.

Answer:

The different card designs possible are:

224

Step-by-step explanation:

It is given that:

There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)

As she has to choose one from each given item this means she will use a combination to choose the item.

We know that the combination for r choices out of total n choices is given as:

[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]

Hence, the total combinations made are given as:

[tex]2_C_1\times 4_C_1\times 7_C_1\times 4_C_1\\\\\\=\dfrac{2!}{1!\times (2-1)!}\times \dfrac{4!}{1!\times (4-1)!}\times \dfrac{7!}{1!\times (7-1)!}\times \dfrac{4!}{1!\times (4-1)!}\\\\=2\times 4\times 7\times 4\\\\=224[/tex]

Hence,  the different card designs that are possible are:

224

The different card designs that are possible will be 224. The formula for the combination is used to solve the problem.

A permutation is an act of arranging the objects or elements in order.

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

The given data in the problem is;

Paula is going to choose 2 sizes, 4 colors, 7 phrases, and 4 pictures . If the one item has to be chosen;

The total combination is;

[tex]= \rm 2C_1 \times 4C_1 \times 7C_1 \times 4 C_1 \\\\ = \frac{2!}{1!\times (2-1)!} \times \frac{4!}{1! \times (4-1)!} \times \frac{7!}{1!\times (7-1)!} \times \frac{4!}{1!\times (4-1)!} \\\\ =2 \times 4 \times 7 \times 4 \\\\ =224[/tex]

Hence different card designs are possible will be 224.

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Answer: False

Solution:

The exponential functions with the form y=a^x never cross the x-axis (x-axis is an asymptote), but in this case we have the exponential function translated 4 units downward, then this function crosses the x-axis.

As it is not given a is positive real number or negative real number.

By supposing a is any real number, we will draw the graph of the curve

[tex]a^x-4[/tex] by taking different values of x.

As i have taken different values of a ,

I found that for a< 0, the graph of the curve [tex]y=a^x-4[/tex]  does not exist.

For any other value of a, the curve cuts the x axis at one point.

For values of 1<a<0, the curve will cut negative side of X axis.

For value of a, a≥1, the curve will cut positive side of X axis.

For , a=0, the curve will not cut the x axis.

So, The function , f(x)=[tex]a^x -4[/tex] will cuts the x axis at one point for a >0 and for negative values of a, and for a< 0 ,it will not cut the x axis.

Answer:  The volume of the pyramid is measured in cubic yards.

Step-by-step explanation:  Given that the dimensions of a square pyramid are measured in yards.

We are to find the unit in which the volume of the pyramid is measured.

We know that

the volume of a square pyramid with length of base edge 'a' units and height 'h' units is given by

[tex]V=\dfrac{1}{3}a^2h~\textup{cubic units}.[/tex]

Here, length of base edge 'a'  and the height 'h' of the given square pyramid is measured in yards.

Therefore, the volume of the pyramid will be measured in

[tex]\textup{yards}\times \textup{yards}\times \textup{yards}\\\\=\textup{cubic yards}.[/tex]

Thus, the volume of the square pyramid is measured in cubic yards.

Answer: I saw someone else answer this and it doesn't match up with the choices so I decided to do this my self and for anyone else who might need this in the future. For those on Khan academy the answers are B, C, AND D.

Step-by-step explanation: I found the unit rate of 350 and 5, because we can use a calculator (as stated on top) I just punched in 350 divided by 5 and got 70. Now i know this may not sound that "professional", but nothing needs to always be professional as long as its efficient and most importantly gets you the right answer. I then took the time to multiply each number, (the ones on the left : 3, 3.5, 6, 7.25, and 8) by 70. If the answer you got on the calculator match up to the number on the right, (240, 420, 507.50, and 490) its correct, if it doesn't match up, you can tell that its most likely not the answer. You should end up with three answers that all end up having the unit rate of 70. Hope this helps anyone who needed it.

ANSWERS ARE B, C, AND D.

Following could be combinations of values for the plumber's work hours and total work fee she charges : 8 hours and $490, 7.25 hours and $500, 270 for 3 hours work. So, the correct choice of options for the image are B, C, and D.

Since the relationship between the number of hours a plumber works and the total work fee he charges is proportional, we can use the following equation to calculate the total work fee:

Total work fee = Number of hours worked * Hourly rate

Therefore, the following combinations of values for the plumber's work hours and total work fee are proportional:

8 hours and $490 (the hourly rate is $490/8 hours = $61.25)

7.25 hours and $500 (the hourly rate is $500/7.25 hours = $68.75)

6 hours and $420 (the hourly rate is $420/6 hours = $70)

The other two options, A and E, are not proportional.

For example, if the plumber works for 3 hours and charges $245, the hourly rate would be $245/3 hours = $81.67.

However, if the plumber works for 3.5 hours and charges $270, the hourly rate would be $270/3.5 hours = $77.14.

This shows that the hourly rate is not constant, so the relationship between the number of hours worked and the total work fee is not proportional.

The correct choice of options for the image are B, C, and D.

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Answer:

Step-by-step explanation:

17.5

Therefore, the solution for c in terms of P and s is c = s(1 - P).

To solve for c in the equation P = (s - c) / s, you want to isolate c on one side. Here's the step-by-step:

Multiply both sides by s to eliminate the denominator: P × s = s - c.

Distribute P within s: Ps = s - c.

Now, get all terms containing c on one side: c = s - Ps.

So, the solution for c in terms of P and s is c = s - Ps, or c = s(1 - P).

Answer:

Option B. 8N + 2

Step-by-step explanation:

Expression given in the question is " the sum of 8 times a number and two" will be = (8 times N + 2)

= 8N + 2

Therefore, option B. is the answer.

Using the relationship between force and acceleration, the average force exerted on the ball by the glove is :55.875 N

Given the Parameters :

Recall :

Force = (mΔv ÷ t)

Inputting the Values into the equation :

Force = [0.149 × (15 - 0)] ÷ 0.040

Force = (0.149 × 15) ÷. 0.040

Force = 2.235 ÷ 0.040

Force = 55.875 N

Therefore, the force exerted is 55.875 N

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