Jamie is the accountant of a logistics company. In the month of December, $5,000 of wages remained unpaid. The accounting period

Answer:

The diagram displaying triangle ABC and the relevant statement along with the answer options is attached.

According to this, the answer is: The length of DC is 28.

Explanation:

From the diagram and the data that segment AB equals segment AC, you comprehend that angles B and C of the isosceles triangle ABC are congruent.

Triangles BED and CFD possess two sets of congruent angles (angle B is congruent to angle D, and angles BED and DFC are congruent), indicating that triangles BED and CFD are similar.

This similarity leads to the proportional relationship:

• DE / DF = DB / DC

Given that the ratio of DE to DF is 5:7, we have:

• 5/7 = DB / DC

Also, it is stated that segment BC is 48.

From the figure:

• BC = DB + DC = 48.

This results in two equations:

• 5/7 = DB / DC

• DB + DC = 48.

Now, we define DC = x, which implies DB = 48 - x, leading to the equation:

• 5 / 7 = (48 - x) / x

Solve this:

• 5x = 7 (48 - x)... [multiplication property: multiply by x and 7]

• 5x = 336 - 7x... [distributive property]

• 12x = 336... [addition property: add 7x to both sides]

• x = 336 / 12... [division property: divide by 12]

• x = 28... [simplification]

Therefore, the length of segment x = DC = 28.

The outcome is $7.54 for each book.

By adding 1137.5 and 1500, you obtain 2637.5.
Then, dividing 2637.5 by 350 gives 7.54.

Verifying the result
350 multiplied by 7.54 equals $2639.

Subtracting $1137.5 from $2639 results in $1501.5 (profit).

Indeed, a fare of $40 is a fair charge for the cab ride.

Explanation

Sheri's cab fare totaled $32, with a gratuity rate of 20%.

The gratuity amount is:

Thus, the total cab fare including gratuity is:

Since Sheri issued a $40 check to the cab driver, it indicates she provided ($40 - $38.40) or an extra $1.60 to the cab driver. Consequently, the $40 payment is reasonable for the cab fare.

Answer:

E(t) = [ 4cos(t), 2 sin(t) ]

Step-by-step explanation:

The equation for the ellipse can be represented as:

 (x² ÷ a² ) + (y² ÷ b² ) = 1    Here, a and b symbolize the semi-major and semi-minor axes.

In this specific instance, we have    x²/16 + y²/ 4 = 1

This expression indicates that it follows the form of (x/a)² + (y/b)² =1

Specifically in our case,    x²/16  + y²/4 = 1, which resembles                 sin²α + cos²α = 1.

By setting x = 4 cos(t), we can proceed to calculate y.

Utilizing the equation x²/16  + y²/4 = 1, we find that:

x²/16  + y²/4 = 1   ⇒    (x²  +  4y²) ÷ 16  = 1

Solving for y yields: (x²  +  4y²)  = 16    ⇒  y²  = ( 16 - x²) ÷4

Substituting x = 4 cos(t) gives us y²  =  (16 - 16cos²(t)) ÷ 4, leading to y = √4 (1 - cos²(t)).

Consequently, we have y = 2 sin(t).

Thus, the vector parameterization of the ellipse can be stated as:

E(t) = [ 4cos(t), 2 sin(t) ]

Answer: D)

Step-by-step explanation:

Based on the provided information, we have

Sample size: n= 15

sample mean:

Sample standard deviation: s= $20

Since the population standard deviation is not known, we utilize a t-test.

For a significance level of 95% confidence:

Critical t-value :  [Using the Student's t-value table]

The required 95% confidence interval yields:-

Thus, the sought-after 95% confidence interval for the mean amount spent by credit card customers during their initial visit to the new store in the mall, assuming normal distribution of the spending amounts, is: