1.The sales tax rate in a certain state is 8%. How much would you pay in total for a taxable item that costs $25.25?

2.Alicia answered 20 out of 25 problems correctly on a test. What percent did she get correct?

3.Jim bought a fishing rod for $42. This price was 70% of the original price. What was the original price?

4.An auctioneer sold items totaling $42,000. If her rate of commission was 7%, what was her income from commissions?

5.At a local hardware store, Ms. Jones learned that 1 would cost her $.50, 12 would cost $1.00, and the price of 144 would be $1.50. What was Ms. Jones buying?

6.People sometimes use credit cards to purchase items they can’t afford to pay for at the moment of purchase. If you’re one of these people, you should know that the monthly finance charge on credit purchases is based on percent. Let’s say you have an outstanding balance of $800 on your credit card. The credit card company charges 1.6% per month. What finance charge will you have to pay for one month?

The orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.

Orbital period of a body is the the time taken by a body to cover one circular path around the central object under whose influence it is following circular path.

Given is a asteroid moving around the sun.

Mean distance from the Sun [x] = 10 AU = 1.496 x 10¹² m.

Assume that the time period of the asteroid is T.

The formula to calculate the orbital period around the sun is -

T²/ R³ = 4π²/GM[s]

Where -

R is the mean distance from sun.

G is the universal Gravitation constant.

M[s] is the mass of Sun.

Substituting the values, we get -

T² = (1.496 x 10¹² x 4 x 3.14 x 3.14)/(6.673 x 10⁻¹¹ x 1.98 x 10³⁰)

T² = (59 x 10¹²)/(13.2 x 10⁻¹⁹)

T² = 4.45 x 10 x 10³⁰

T² = 44.5 x 10³⁰

T = √44.5 x √10³⁰

T = 6.7 x 10¹⁵ seconds

In years, the time period will be -

T = 212314723 years (approx.)

Therefore, the orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.

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Answer:

B 12.5 < x < 18.9

Step-by-step explanation:

HL congruence theorems or postulates used to prove ΔLMN ≈ΔOPQ.

Congruent figures have sides that are the same length and angles that are the same measurement. In other words, congruent figures are those in which one figure superimposes another.

If two line segments have the same length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If the matching sides and angles of two triangles are equal, they are said to be congruent.

We have two Triangles as ΔLMN and ΔOPQ

As, per the figure both triangles are Right angles Triangle.

Also, LM = OP

MN = PQ

LN = OQ

and, the hypotenuse of both triangles also Equal.

Thus, both triangle are Congruent using HL theorem.

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The inequality representing Andrew's spending limit is d <= $3.25, where d is the daily spending amount for the remainder of the week. Solving this, Andrew can spend at most $3.25 per day for the next 4 days.

Andrew received a weekly allowance of $17.50. He spent $4.50 on lunch on Monday. The question is how much at most can he spend each day for the remaining 4 days if he spends the same amount each day. To answer this, we subtract the amount spent on Monday from the total weekly allowance to find the remaining balance. Then, we divide this remaining balance by the number of days left in the week to find the daily spending limit:

Total allowance = $17.50

Spent on Monday = $4.50

Remaining balance = Total allowance - Spent on Monday
= $17.50 - $4.50
= $13.00

Days left in the week = 4

Daily spending limit = Remaining balance \/ Days left
= $13.00 / 4
= $3.25

The actual answer to this problem is (4.8,7.6)

Using the internal division formula the coordinates of the ball are (4.8,7.6).

Let us assume the x-axis as the goal line and the y-axis as the sideline

So, coordinates Messi≡(3,4)

Similarly, coordinates Suarez≡(6,10)

Let us suppose the ball is somewhere in between Messi and Suarez

Suppose coordinates of the ball ≡(a,b)

Since the ratio between the distance between Messi and the ball to the distance between Suarez and the ball is 3/2.

This means ball is internally dividing Messi and Suarez in 3:2

So, applying the internal division formula for a straight line.

If a point (a,b) is internally dividing a line segment with coordinates of endpoints as (x₁,y₁) and (x₂,y₂) in the ratio m:n then

[tex]a= \frac{m_{1}x_2+m_2x_1 }{m+n}[/tex]

[tex]a= \frac{m_{1}y_2+m_2y_1 }{m+n}[/tex]

So, [tex]a = \frac{3*6 + 2*3}{3+2}[/tex]

[tex]a=4.8[/tex]

[tex]b= \frac{3*10+2*4}{3+2}[/tex]

[tex]b=7.6[/tex]

So, the coordinates of the ball≡(4.8,7.6)

Therefore, Using the internal division formula the coordinates of the ball are (4.8,7.6).

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Final answer:

The sum of the rational expressions is found by obtaining a common denominator, combining the numerators, and simplifying the resulting expression. The correct answer is [tex](8x^2-9x)/(x^2+3x-10).[/tex]

Explanation:

The sum of the rational expressions [tex]x/(x-2) + 7x/(x+5)[/tex] requires finding a common denominator before the sum can be calculated.

The common denominator for these two fractions is the product of the individual denominators (x-2) and (x+5), which is [tex]x^2+3x-10.[/tex]

Once we have a common denominator, we can combine the numerators and simplify the expression as follows:

Multiply the first term by (x+5)/(x+5) and the second term by (x-2)/(x-2) to create a common denominator.

Combine the numerators: [tex]x*(x+5) + 7x*(x-2)[/tex]

[tex]= x^2+5x + 7x^2-14x[/tex]

[tex]= 8x^2-9x.[/tex]

Place the combined numerator over the common denominator: [tex](8x2-9x)/(x^2+3x-10).[/tex]

Therefore, the correct sum of the given rational expressions is option c. [tex](8x2-9x)/(x^2+3x-10).[/tex]

The modulo operator determines the remainder of a division operation. For the given expressions, the results are a. 1, b. 4, c. 2, d. 6

The question is asking to evaluate several expressions using the modulo operation. Modulo is a mathematical operation that finds the remainder or signed remainder of a division, after one number is divided by another (called the modulus). Here's how we can solve each:

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Answer:

9 + 7 + 6 + 2 + 2 + 1 = 27 ÷ 6 = 4.5

4.5 - 9 = 4.5

4.5 - 7 = 2.5

4.5 - 6 = 1.5

4.5 - 2 = 2.5

4.5 - 2 = 2.5

4.5 - 1 = 3.5

4.5 + 2.5 + 1.5 + 2.5 + 2.5 + 3.5 = 17 ÷ 6 = 2.83 or 2.8

so our MAD is 2.83 or 2.8!

Answer:

Zero

C is the correct option.

Step-by-step explanation:

In the given graph, the given lines are parallel to each other and hence never intersect.

Now, we know that the intersection point (s) of two curves gives us the solution.

Here the lines are parallel to each other and hence do not intersect each other.

Thus, there would not be any intersection point.

Hence, the system of equations has no solution.

C is the correct option.

As g(x) is a function that is multiplied by - 1 with f(x) D. They are reflections of each other over x = y.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, g(x) is a function that is multiplied by - 1 with f(x).

∴ f(x) = - g(x).

So, They are reflections of each other over x = y.

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Answer:

Step-by-step explanation:

Answer:

8.2%

Step-by-step explanation:

o-ware