Help..........................

Answer:

f^-1(x) = 1/5 x

Step-by-step explanation:

y = 5x

Exchange x and y to find the inverse

x = 5y

Solve for y

1/5x = y

The inverse is 1/5x

Answer:

\(\Large \boxed{f^{-1}(x)=\frac{x}{5} }\)

Step-by-step explanation:

f(x) = 5x

Replace f(x) with y.

y = 5x

Switch variables.

x = 5y

Divide both sides by 5.

\(\frac{x}{5} =y\)

The number of cars in the parking lot at 5 pm is 106.1.

The formula for the number of cars in the parking lot n hours after 3 pm is:

\(A_{n} = 92(1.09)^n\)

where:

\(A_{n}\) is the number of cars in the parking lot n hours after 3 pm

92 is the initial number of cars in the parking lot

1.09 is the growth rate of the number of cars in the parking lot

n is the number of hours after 3 pm

For example, if it is 5 pm, then n = 2. Plugging this value into the formula, we get:

\(A_{5} = 92(1.09)^2\)

\(A_{5} = 106.1\)

Therefore, the number of cars in the parking lot at 5 pm is 106.1.

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Answer:

p=48.

Step-by-step explanation:

Divide 96 divided by 2 which will give you 48. So the answer will be p=48.

The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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Answer:

\(h = 7.69cm\)

Step-by-step explanation:

Given

\(Volume = 455cm^3\)

\(l = h\)

Where:

\(h \to height\)

\(l \to base\ length\)

Required

The height

The volume is calculated as:

\(Volume = l^2 * h\)

This gives:

\(Volume = h^2 * h\)

\(Volume = h^3\)

Rewrite as:

\(h^3 =Volume\)

So, we have:

\(h^3 = 455cm^3\)

Take cube roots

\(h = \sqrt[3]{455cm^3}\)

\(h = 7.69cm\) --- approximated

Answer:

Cubic, Binomial

Step-by-step explanation:

A cubic function is when the degree of the polynomial is 3

The degree is the highest power

A binomial has 2 terms

So 8x^3-1 is a binomial and is cubic

Answer:

2/15

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

12 & 18 can be reduced to 2 & 3

25 & 5 can be reduced to 5 & 1

2/5 × 1/3 = 2/15

Answer:

A.    48 + 2x = 180

Step-by-step explanation:

This is an isosceles triangle

Therefor the unmarked angle is also xº

The three angles are 48, x and x

The total of the angles in a triangle is 180

48 + x + x = 180

48 + 2x = 180

Answer: 3 servings

Step-by-step explanation:

Sam used 2 cups of pineapple juice, one serving just needs 2/3 cups of pineapple. 2 divided by 2/3 equals 3 so, Sam made three servings. (in this case 1/2 cup orange juice 3/4 cup Lemon/lime juice 1/3 cup Ginger ale does not matter, you only need to know the pineapple juice.

Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

slope = (y2-y1)/(x2-x1)

\( \frac{ - 1}{7} = \frac{n - 10}{ - 1 - - 3} = \frac{n - 10}{2} \)

\( \frac{ - 2}{7} = n - 10 \)

\( - 2 = 7n - 70 \\ 7n = 68 \\ n = 9.7\)

Without a coupon and paying $90 the customer was attended for 2 hours

When a customer with a coupon for 40% off the inspection fee pays $110 for a 4-hour repair the inspection fee is calculated

customer's pay =  (inspection fee * 40% off the inspection fee)  + charge per hour  * number of hours

40% off  means the customer paid 60% of the fees

let the inspection fee be x

110 = (x * 0.60)  + 20 * 4

110 = 0.6x + 80

110 - 80 = 4x

0.6x = 30

x = 50

a customer without a coupon

let the number of hours be y

customer's pay =  inspection fee + charge per hour  * number of hours

90 = 50 + 20 * y

90 = 50 + 20y

20y = 90 - 50

20y = 40

y = 2

the customer spent 2 hours

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Answer:

I think it's 18

Step-by-step explanation:

because I'm looking at 12/8 to be a ratio, that means that the size of the bigger figure had decreased by 12/8 or 1.5

then I divided the 27 by 1.5 to get the area of the small one which was 18.

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

\(= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}\)

Now we will put the values into the above formula

\(= \frac{\$9:00}{6}\)

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

Applying the inscribed angle theorem, the measure of angle BAC is: 110°.

According to the inscribed angle theorem, the measure of angle BAC is half the measure of the intercepted arc, x + 50°.

x - 30 + x + 50 = 360

2x + 20 = 360

2x = 360 - 20

2x = 340

x = 170

m∠BAC = 1/2(x + 50)

Plug in the value of x

m∠BAC = 1/2(170 + 50)

m∠BAC = 110°

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"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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Answer:hi

Step-by-step explanation:

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Answer:

Step-by-step explanation:

ft7654

Answer:

first let's solve for x

x + (x + 30) + 2x = 180

4x + 30 = 180

-30          -30

4x = 150

/4      /4

x = 37.5

Now solve for the angle measures:

(x + 30)    =    (37.5 + 30) = 67.5

2x       =        2(37.5) = 75

x = 37.5

Answer:

X= 37.5

Step-by-step explanation:

Answer: 26 degrees, 51 degrees, 103 degrees

Step-by-step explanation:

The sum of the angles of triangles all equal exactly 180 degrees; no more or no less. Therefore, just add 26, 51, and 103 degrees to get your sum: 180 degrees.

Based on this theorem, the answer above is correct.

Answer: (0,10)

Step-by-step explanation: y=mx+b

y=12.5x+10

0=12.5x+10

10 is y because its on the outside

Answer:

c < 3

Step-by-step explanation:

We can first add 10 to both sides to remove the -10.

This is additive property of equality, where both sides must stay the same ratio, so we always use the same property on both sides unless simplifying what is already there.

So we now have c + 3c < 12.

As I mentioned less than 2 full sentences above, we can simplify without doing the same thing to both sides if it is already there, so we can add the c + 3c since it is already there.

We now have 4c < 12.

Then, we divide both sides by 4 to get c, and again mentioned about 4 sentences above, we need to divide both sides.

So we now should have c < 3.

NOTE: IF YOU HAVE A SIMILAR PROBLEM WHERE THE VARIABLE IS NEGATIVE LIKE -4a FOR EXAMPLE, THE INEQUALITY SIGN CHANGES DIRECTION. IN THIS PROBLEM, THAT IS NOT THE CASE, BUT FOR FUTURE PROBLEMS, THAT IS A MUST.

:D

Answer:

8500

Step-by-step explanation:

When compounded continuously the future value,  FV , of your initial investment,  PV , is determined with the the equation

\(FW = PV\) ×\(e^{rxt}\)

where  r  is the norminal interest rate, expressed as a decimal, and  t  is the investment period in years.

Plugin the values in this equation gives

\(FW = $7,500\) × \(e^{0.015x8} =$8,456.23\)

Round to nearest hundred dollars = 8500

The equation of circle is x² + y² = 36.

We have,

Center= (0, 0)

Passing point = (0, 6)

We know the equation of circle is

(x-h)² + (y-k)² = r²

where (h, k) be the center and r be the radius.

Now, the radius of circle is

= √(6-0)² + (0-0)²

= √36

= 6 unit

So, the equation of circle

(x-0)² + (y-0)² = 6²

x² + y² = 36

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The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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