Suppose that you work part-time as a sales representative at a car dealership. You earn a base salary of $125 per week plus a 18% commission on all sales that you make. Your best friend has exactly the same job at another car dealership but earning a base salary of 85$ per week plus a 21% commission on all sales. How much do you and your friend need to sell in order to earn the same amount in any given week?

Final answer:

The truck driver can travel 700 miles on 35 gallons of gas.

Explanation:

In order to determine the distance the truck driver can travel on 35 gallons of gas, we can set up a proportion using the information provided.

The truck driver can travel 560 miles on 28 gallons of gas, so we can set up the proportion:

= 560 miles / 28 gallons

= x miles / 35 gallons.

Cross-multiplying and solving for x, we find that x = 700 miles.

Therefore, the truck driver can travel 700 miles on 35 gallons of gas.

The Overall Change in score is 9.9 points.

What is overall change?

Overall Change is the difference of initial average and final average.

Given that you are playing a game and lose 4.8 points and again loose 7.6 points and finally win 2.5 points.

According to question we have

4.8 + 7.6 = 12.4

Then 12.4 - 2.5 = 9.9 points

Hence, Overall Change in the score is 9.9 points.

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The equation 4(2x + 3y) = 4(3y + 2x) is representing the Commutative Property of Addition, which means the order in which you add numbers does not change the sum.

The equation in your question, 4(2x + 3y) = 4(3y +2x), is an example of the Commutative Property of Addition. This property means that the order in which you add numbers does not change the sum. In this case, (2x + 3y) and (3y + 2x) are the same because of the Commutative Property of Addition, the order of 2x and 3y doesn't impact the result. The multiplication by 4 on both sides does not change this property being applied.

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Identify the complete predicate in the sentence below.

traveled west in covered wagons.

Identify the simple subject and verb

lines provided

The correct answers are:

Complete predicate: a. "traveled west."

Simple subject and verb: a. "lines provided."

For the sentence "The settlers traveled west in covered wagons":

The complete predicate is: a. "traveled west."

Now, for the sentence "Soon, telegraph lines provided additional communication to the city":

The simple subject is "lines."

The verb is "provided."

So, the correct option is: a. "lines provided."

This simple subject and verb combination makes up the core of the sentence, indicating what the sentence is about and what action is taking place.

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Answer:

The ratios for sin a and cos  a is  [tex]\frac{7}{24}[/tex] .

Step-by-step explanation:

As given the expression in the question be as follow .

[tex]sin\ a = \frac{14}{50}[/tex]

[tex]cos\ a = \frac{48}{50}[/tex]

Thus the ratio of the sin a and cos  a .

[tex]\frac{sin\ a}{cos\ a} = \frac{\frac{14}{50}}{\frac{48}{50}}[/tex]

[tex]\frac{sin\ a}{cos\ a} = \frac{14\times 50}{48\times 50}[/tex]

[tex]\frac{sin\ a}{cos\ a} = \frac{14}{48}[/tex]

Simplify the above

[tex]\frac{sin\ a}{cos\ a} = \frac{7}{24}[/tex]

Therefore the ratios for sin a and cos  a is  [tex]\frac{7}{24}[/tex] .

Final answer:

John received 10 nickels, 20 dimes, and 42 quarters.

Explanation:

Let's solve this problem step by step:

Let's assume the number of nickels = x

Number of dimes = x + 10 (10 more dimes than nickels)

Number of quarters = x + 10 + 22 (22 more quarters than dimes)

Given that the total value of change is $13, we can form the equation:

0.05x + 0.10(x + 10) + 0.25(x + 10 + 22) = 13

Simplifying the equation, we get:

0.05x + 0.10x + 1 + 0.25x + 7.75 = 13

Combining like terms, we get:

0.40x + 8.75 = 13

Subtracting 8.75 from both sides:

0.40x = 4.25

Dividing by 0.40:

x = 10.625

Since we can't have a fractional number of nickels, we round down to the nearest whole number.

Therefore, John received 10 nickels, 10 + 10 = 20 dimes, and 10 + 10 + 22 = 42 quarters.

Answer:

D

Step-by-step explanation:

"the male interquartile is not accurate because the first quartile is missing"

Answer:

3 ≤ x ≤ 7

Step-by-step explanation:

Why, because i said so, and also because i got it right in the quiz

Answer:

3 ≤ x ≤ 7

Step-by-step explanation:

Answer:

Option C is the answer: $3,090.64

Step-by-step explanation:

Lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily.

Means p = 5003.86

r = 3.7% or 0.037

t = 13

n = 365 (assuming there are 365 days in a year)

[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]

[tex]A=5003.86(1+\frac{0.037}{365} )^{4745}[/tex]

=> [tex]A=5003.86(1.00010136)^{4745}[/tex]

A = $8094.09

Interest earned = [tex]8094.09-5003.86=3090.26[/tex] dollars

This is closest to option C, hence, option C is the answer.

The total number of almonds can be represented by the equation:

x = 25b + 7

We can use the information given in the question to set up an equation to represent the total number of almonds.

Let b represent the number of bags, and

let x represent the total number of almonds.

According to the problem, each bag contains 25 almonds, and there are 7 almonds left over. Therefore, the total number of almonds can be represented by the equation:

x = 25b + 7

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Final answer:

To find the dimensions of the can with the least cost, we need to minimize the cost function f(r) = 8πr² + 12πrh. We can find the critical points of f(r), determine the minimum point, and verify it using the second derivative test.

Explanation:

To find the dimensions of the can with the least cost, we need to consider the cost of the top, bottom, and the side of the can. Let's denote the radius of the can as 'r' and the height as 'h'.

(a) The cost of the top and bottom of the can is given by the area of two circles, which is 2 * 4 * π * r² = 8πr² cents. The cost of the side is given by the area of a rectangle, which is 4 * π * r * h * 3 = 12πrh cents. So, the function f(r) that gives the cost of the can in terms of the radius r is f(r) = 8πr² + 12πrh.

The domain of the function f(r) is the set of all non-negative real numbers, since the radius cannot be negative.

(b) To find the radius and height of the can with the least cost, we need to minimize the function f(r). We can do this by finding the critical points of f(r), where the derivative of f(r) with respect to r is equal to zero. Solving f'(r) = 0, we can find the value of r that minimizes the function. Once we have the value of r, we can substitute it back into the function f(r) to find the minimum cost.

(c) We can determine that we have found the can of least cost by verifying that the critical point we found for the function f(r) is a minimum point. We can do this by checking the second derivative of f(r) at the critical point. If the second derivative is positive, then the critical point is a minimum point.

Final answer:

An undo table in mathematics refers to using inverse functions to reverse the effect of their counterpart operations, such as using the square root to undo a square, and logarithms to revert exponential calculations.

Explanation:

An undo table in math refers to a concept rather than a literal table. It encompasses mathematical operations that effectively reverse the effect of their counterparts. For example, to undo a squaring operation, we use a square root; similarly, to reverse an exponentiation, we utilize a logarithm. In essence, these operations are known as inverse functions.

Let's take the scenario of finding the side length of a right triangle. Given the triangle's side b and hypotenuse c, the Pythagorean Theorem states that a² + b² = c². To solve for side a, one would rearrange the equation to a² = c² - b². Then, to find a, we have to undo the square by taking the square root of both sides, resulting in a = √(c² - b²).

Mathematics is not about rote memorization of rules but understanding the logic and relationships between numbers. As such, when faced with the operation of squaring, we 'undo' it by understanding the core concept of square roots. Similarly, subtraction undoes addition, division undoes multiplication, and the inverse functions of trigonometric and exponential expressions undo their respective basic functions.

Therefore, the natural logarithm (ln) and the exponential function are inverses of each other and hence can undo each other as well.

Answer:

a.

Step-by-step explanation:

took quiz

The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is 22 units.

To find the length of the side opposite the \( 30^\circ \) angle in a right triangle with a hypotenuse of 44, we can use the sine function:

1. Identify the Known Angle and Hypotenuse: We have an angle of[tex]\( 30^\circ \)[/tex] and a hypotenuse of 44.

2. Use the Sine Function: Since sine relates the opposite side and the hypotenuse in a right triangle, we use the sine function for the [tex]\( 30^\circ \)[/tex] angle.

[tex]\[ \sin(30^\circ) = \frac{\text{opposite}}{44} \][/tex]

3. Sine of 30 Degrees: The sine of [tex]\( 30^\circ \)[/tex] is a known value, which is [tex]\( \frac{1}{2} \).[/tex]

4. Calculate the Opposite Side: Use the sine value to find the opposite side:

[tex]\[ \text{opposite} = 44 \cdot \sin(30^\circ) = 44 \cdot \frac{1}{2} \][/tex]

5. Result: The length of the side opposite the[tex]\( 30^\circ \)[/tex] angle is therefore:

[tex]\[ \text{opposite} = 22 \][/tex]

Answer:

A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.

C. The ball reaches its maximum height about 4 seconds after it is thrown

Step-by-step explanation:    • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.

• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.

• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.

• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.

• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.

Answer:  the correct option is

(a) If x – 5 ≠ 10, then 4x + 1 ≠ 61.

Step-by-step explanation:  We are given to select the correct inverse of the conditional statement p → q if

p : x – 5 =10  and  q : 4x + 1 = 61.

We know that

the inverse of a conditional statement p → q is given by "not p → not q".

Therefore, the inverse of the given statement is

not p → not q

that is, if  x – 5 ≠ 10, then 4x + 1 ≠ 61.

Thus, the required inverse is " x – 5 ≠ 10, then 4x + 1 ≠ 61."

Option (a) is CORRECT.

Solution: As the line shown in the graph passes through (3,0) and (0,-1).

So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by

→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]

→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]

So ,the equation of line is ,→3 y = x-3

  → x- 3 y -3= 0 or y=x/3 -1

take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S

Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.

it means the above equation can be written as , y≥x/3 -1.

None of the option is correct.

Yes, it is possible to draw a triangle with the angle measures to be; 50, 50 and 80 degrees.

A right angled triangle is a triangle having one of its angle with measure of 90°. If all of three angles of a triangle are < 90° then triangle is acute.

If one of the angle is of 90°  then the triangle is right angled triangle.

If one of the angle is  > 90°  then triangle is called obtuse triangle.

First of all, we need to know a quality of all interior angles of a triangle, they must be add to 180 degrees.

Total = 50 + 50 + 80 degrees

Total = 100+80

Total =180 degrees

Therefore, yes, it is possible to draw a triangle with the angle measures to be; 50, 50 and 80 degrees.

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Answer: She earned $ 4 for each package delivered.

Step-by-step explanation:

Since, her total rate of earning = $ 12.50 per hours,

And, she worked for 8 hours.

⇒ She earned in 8 hours = 8 × 12.50 = $ 100

According to the question,

She delivered 25 packages in 8 hours.

⇒ 25 packages = 8 hours

⇒ 25 packages = $ 100

⇒ 1 package = $ 4

Thus, she earned 4 dollars for each package.

Modulus of a number always yields Positive Result.Modulus is defined is as follows

|x|=x, if x>0.

|-x|=-(-x)=x, if x<0

|x|=0, if, x=0.

 → |-5|=5

⇒The best way of representing , 5 on the number line is

Option C

A number line from negative 5 to positive 5 with increments of 1 is drawn. A horizontal line is drawn from 0 to positive 5, and 5 is written above it.

The student asked for the four smallest positive angles where cosine equals ½. By using the unit circle, the angles of 60° and 300° are identified as solutions, with their general solutions given by θ = π/3 + 2kπ and θ = 5π/3 + 2kπ. The four smallest positive answers are thus 60°, 300°, 420°, and 660°.

The student is asking for the four smallest positive angles θ for which the cosine is equal to ½. To find these angles, it helps to recall the unit circle and the fact that the cosine of an angle corresponds to the x-coordinate of a point on the unit circle. The angles with a cosine of ½ in the first 360° (or 2π radians) are those where the corresponding points on the unit circle are at (½, √3/2) and (½, -√3/2). These points correspond to angles of 60° (or π/3 radians) and 300° (5π/3 radians) respectively. However, these are not the only solutions when considering multiple rotations around the circle.

The general solutions for cosine equaling ½ in terms of radians are given by:

The four smallest positive solutions correspond to setting k=0 and k=1 in the above equations, yielding the angles:

Note that these angles are measured in degrees for simplicity, but they can be converted to radians by using the equivalence 180° = π radians. To convert these angles to radians, simply divide by 180 and multiply by π.

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