1. A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.
(a) A manager, Jake, reasoned that since 32 goes into 64 twice, each employee will get about $2000. Is his estimate correct? Why or why not?
(b) How much will each employee receive, rounded to the nearest whole dollar? Leave the remainder undivided. Show your work.
Answer:

The missing part indicated in the figures are ? = 12, TX = 9 and x = 20

Figure a

The missing part can be calculated using the following equation

?/(11 - 5) = 22/11

Evaluate the difference

?/6 = 22/11

So, we have

? = 6 * 22/11

Evaluate the expression

? = 12

Figure b

The missing part can be calculated using the following equation

TX/3 = 6/2

So, we have

TX = 3 * 6/2

Evaluate

TX = 9

Figure c

The value of x can be calculated using the following equation

1/4x + 6 = 2x - 29

So, we have

x + 24 = 8x - 116

Evaluate

-7x = -140

Divide

x = 20

Hence, the value of x is 20

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Answer: I think it's H, if it isn't and you get a second try it should be N

Step-by-step explanation: Both H and N start with 0/-3 except F which means F is wrong. Maybe you should wait for a better answer...but it shouldn't be F

Answer:

the train will travel 245 feet in 3 and 1/2 seconds

Step-by-step explanation:

To determine the distance the train will travel in 3 and 1/2 seconds, we can use a proportion based on the given information.

Let's set up the proportion:

70 feet / (1/10 second) = x feet / (3 1/2 seconds)

To solve this proportion, we can first convert the mixed number 3 1/2 to an improper fraction.

3 1/2 = 7/2

Now we can rewrite the proportion:

70 / (1/10) = x / (7/2)

To simplify the proportion, we can multiply the numerator and denominator of the right side by 10/1:

70 / (1/10) = (x * 10) / (7/2)

Simplifying further, we get:

70 * (10/1) = x * (10/7/2)

700 = x * (20/7)

To find x, we can divide both sides of the equation by (20/7):

x = 700 / (20/7)

x = 700 * (7/20)

x = 245 feet

Therefore, at the same speed, the train will travel 245 feet in 3 and 1/2 seconds.

Mark's cost does not vary directly with time spent talking, it indicates the presence of other factors, such as pricing structure, additional services, peak hours, bundled packages, or promotions, that influence the overall cost. These factors can lead to non-linear cost variations and a lack of direct proportionality between the cost and time spent talking.

If Mark's cost does not vary directly with the time spent talking, it means that there is not a simple proportional relationship between the two variables. In other words, doubling the time spent talking does not necessarily result in doubling the cost. This indicates that there are other factors influencing Mark's cost besides just the time spent talking.

There can be several reasons why Mark's cost does not vary directly with time spent talking:

Pricing structure: Mark's cost may be determined by a pricing structure that includes fixed fees or additional charges based on certain conditions. For example, there might be a base rate for a certain duration of talk time, and any additional time may be billed at a different rate.

Additional services: Mark's cost might include additional services or features that are not solely dependent on talk time. For instance, there could be charges for international calling, call forwarding, or other value-added services.

Peak hours or special rates: Mark's cost might be affected by peak hours or special rates. Some service providers offer different pricing during certain times of the day or specific days of the week. This could result in non-linear cost variations with respect to time spent talking.

Bundled packages: Mark's cost might be part of a bundled package that includes other services like internet or television. In such cases, the overall cost may be influenced by factors other than talk time.

Promotions or discounts: Mark's cost may be subject to promotional offers or discounts that are not directly related to the time spent talking.

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The comparison of the functions is

From the question, we have the following parameters that can be used in our computation:

The graph of the two functions

For the linear function, we have

y-intercept = 0

Rate = 50/1 = 50

So, the function is

y = 50x

For the exponential function, we have

y-intercept = 1

Rate = 250/150 = 5/3

So, the function is

y = (5/3)ˣ

Comparing the functions, we have

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Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.

To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.

Let's calculate the daily balances for each day:

Day 1: Closing Balance = $850

Day 8: Closing Balance = $300

Day 16: Closing Balance = $500

Day 24: Closing Balance = $650

To calculate the daily balances, we need to consider the activities that occurred on each day.

On Day 1, there was no activity recorded, so the closing balance remains at $850.

On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.

On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.

On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.

Now, let's calculate the average daily balance:

Sum of daily balances = $850 + $300 + $500 + $650 = $2300

Number of days in the billing period = 31

Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19

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Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

The length of side X in simple radical form with a rational denominator is 25/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 5 × 5/√3

Hypotenuse, x = 25/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

Your overall grade, rounded to the nearest hundredth, is approximately 86.35%.

To calculate your overall grade, we need to assign weights to each category and then calculate the weighted average based on your scores.

Let's assume your scores in each category are as follows:

Tests: 85%

Quizzes: 90%

Projects: 92%

Participation: 80%

Final Exam: 88%

Now, let's calculate the weighted average:

Tests: 15% weight × 85% score = 12.75

Quizzes: 10% weight × 90% score = 9.00

Projects: 35% weight × 92% score = 32.20

Participation: 35% weight × 80% score = 28.00

Final Exam: 5% weight × 88% score = 4.40

Overall Grade = Sum of weighted scores / Total weight

Overall Grade = (12.75 + 9.00 + 32.20 + 28.00 + 4.40) / 100

Overall Grade ≈ 86.35%

Therefore, your overall grade, rounded to the nearest hundredth, is approximately 86.35%.

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The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

The inequality corresponding to the equation -4x + y = -3 is either y > 4x - 3 or y < 4x - 3, depending on the relationship between 4x - 3 and 0.

To write the inequality represented by the equation -4x + y = -3, we first need to manipulate the equation to express y in terms of x.

Starting with -4x + y = -3, we isolate y by adding 4x to both sides:

y = 4x - 3

Now we have y expressed in terms of x. To form the inequality, we consider the relationship between x and y. The inequality depends on whether the expression 4x - 3 is greater than or less than 0.

If 4x - 3 is greater than 0, then y is greater than 0, and we can write the inequality as:

y > 4x - 3

If 4x - 3 is less than 0, then y is less than 0, and we can write the inequality as:

y < 4x - 3

The inequality represents a region in the coordinate plane where the y-values are either greater than or less than the expression 4x - 3, depending on the direction of the inequality sign.

For example, if we choose a point (x, y) in the region above the line y = 4x - 3, where y is greater than 4x - 3, the inequality y > 4x - 3 will hold true. On the other hand, if we choose a point below the line, where y is less than 4x - 3, the inequality y < 4x - 3 will be satisfied.

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The coordinates of the vertices for the image of the pre image is translated 4 units right are:

C. A' = (-1,2), B' = (5, 3), C' = (1,0)

A geometric transformation involves taking a geometric object as input and producing a new geometric object as output. We have different types of geometric transformations such as translation, rotation, reflection etc.

A translation moves a geometric object a certain distance in a certain direction. Translation to the right means movement in the positive x-direction.

Thus, the coordinates of the vertices for the image of the pre image if it is translated 4 units right can be obtained by adding 4 to x-coordinate values while y-coordinate values remain the same. That is:

A(-5,2) becomes A'(-5+4, 2) = (-1,2)

B(1,3)becomes  B'(1+4, 3) = (5, 3)

C(-3,0) becomes C'(-3+4, 0) = (1,0)

Therefore, the coordinates of the vertices of the image of triangle ABC after it is translated 4 units right are (-1, 2), (5, 3), and (1, 0).

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Answer:

100

Step-by-step explanation:

#20 naira - 20 * 100

= 2000kobo

2000/20

100

QED✅✅

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