One number is five more than another. Their sum is thirteen. Find both numbers.


(smaller value)

(larger value)

The GCF is 2cd^2e^3

====================================================

Explanation:

For now, we'll focus on the coefficients. These are the numbers to the left of the variable terms.

The coefficients are: 10, -16, 4

Find the prime factorization of each coefficient:

Notice that each prime factorization has exactly one copy of "2" and nothing else in common, which means the GCF of 10, 16, and 4 is 2. You can use a factor tree to help verify this.

Therefore, the final coefficient we'll factor out is 2.

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Now onto the variable terms.

The variable terms are: cd^4e^3 and c^2d^6e^3 and c^5d^2e^4

Focus on the c terms and they are: c, c^2, c^5

The GCF of the c terms will be the one with the smallest exponent. So that would be c.

The d terms are d^4, d^6, d^2. Circle d^2 since that involves the smallest exponent.

The e terms are e^3, e^3, e^4. The GCF of the e terms is e^3 because we circle the smallest exponent.

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Summary so far:

The GCF of each piece is glued together to get the overall GCF.

The overall GCF is 2cd^2e^3

What do we do with this GCF? We will divide each original term by the GCF to help us factor out the GCF.

\(\frac{10cd^4e^3}{2cd^2e^3} = 5d^2\\\\\frac{-16c^2d^6e^3}{2cd^2e^3} = -8cd^4\\\\\frac{4c^5d^2e^4}{2cd^2e^3} = 2c^4e\\\\\)

Those results are then what's left in the parenthesis after factoring out the GCF.

So we have this final answer

2cd^2e^3(  5d^2  - 8cd^4  + 2c^4e )

The answer can be confirmed by distributing the outer term back through to each inner term.

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

It is 6mn² if you want to know the greatest common factor.

Step-by-step explanation:

Let me start with the coefficients. Since 6 can divide all coefficients, we should pick 6.

For the variables, the least power of m found in the expression is m¹ or simply m.

The least power of n found in the expression is n². Wrapping this up, you get 6mn².

But the expression has many common factors.

e.g. 2, 3, 6, m, n, n², . . .

You can also say -2, -3, -6, -m, -n, -n².

Generally, you may have many common factors, but you will have only one greatest common factor.

The correct answer is March, as it was the month in which the average number of hours worked by the website designers was closest to 50 hours.

A month is a unit of time typically consisting of 30 or 31 days. It is used for measuring periods of time, for example, when we say something happened "a month ago". Months are used in both the Gregorian calendar and the Julian calendar.

This data was gathered from a survey of website designers, which was conducted to determine the average number of hours each month that these professionals spent working.

In January, the average number of hours worked was 46.5. In February, it was 48.8. However, in March, the average number of hours worked was 49.4, which was the closest to 50 hours. This was followed by April, in which the average was 49.7.

Overall, it can be concluded that March was the month in which the average number of hours worked by website designers was closest to 50 hours. This is important data for website designers, as it allows them to understand the amount of time they should be spending on their work in order to be successful. It also helps employers gauge the workload of their website designers and ensure they are providing an adequate amount of work.

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Answer:

$23.12

Step-by-step explanation:

With breakfast included the total would be $142.99. Without breakfast it would be $119.87. So to get the difference it would be:

$142.99 - $119.87 = $23.12

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

Answer:

The correct statements are:

A) There are no zeroes

D) The vertex is (1, 14)

H) The axis of symmetry is x = 1

J) The "a" of the parabola is positive

M) The parabola has a minimum

Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.

Step-by-step explanation:

Step-by-step explanation:

Remember that, this is quadratic function graph.

Let's analyze fact the graph. We get :

There are two roots/zeroes

Two roots are x1 = -2 , x2 = 6

Vertex is maximum value of parabola (2,14)

Symmetry function is x = 2 (you can show that, x-axis from vertex)

"a" parabola indicated negative

The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))

Conclusion :

The true statements are C,F,I,K,N,O (6 statements are shown)

Subject : Mathematics

Level : JHS

Chapter : Quadratic Functions

Answer: Margin of Error for the given CI is 0.08

Step-by-step explanation:

Given the data in the question;

it is a symmetric class interval hence, sample proportion p = (0.50 + 0.66) / 2

p = 1.16 / 2

sample proportion p = 0.58

Margin of Error E will be;

E = 1/2 × length of Confidence interval

Margin of Error E = 1/2 × ( 0.66 - 0.5)

Margin of Error E = 1/2 × 0.16

Margin of Error E = 0.08

Therefore; Margin of Error for the given CI is 0.08

The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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The smallest positive debt that can be paid off using sticker trading is $7$ dollars.

To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.

Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.

The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.

In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.

Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.

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Answer:

Step-by-step explanation:

Volume of cube = side * side *side

                         = 4 * 4 * 4

                         = 64 cubic cm

Answer:

6907 people on that program must be surveyed if we want mean weight loss as 0.25 lb and standard deviation as 10.6 lb.

Step-by-step explanation:

Given that mean of weight loss in 0.25 lb and standard deviation is 10.6 lb.

For 95% confident level z-score must be 1.96.

That is =1.96

Now required sample size is

Where SE means standard deviation=10.6 lb and mean m=0.25 lb

Hence sample size=

Which we always should round up that is 6907.

Answer:

the amount added to the cost price of goods to cover overhead and profit.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Meaning in my own words: The amount applied to the depreciation and production factor price of the product.

Example: Sells for $126 costs $100. Price is increase.

Synonyms for markup: increase, Profit

Hope this helps.

Answer:

Angle sum Theorem says that the sum of the measures of the interior angles of a triangle is 180 degrees. ... This creates alternate interior angles that are congruent. Sum of two interior angles equals the opposite exterior angle...33 + 87 = yy = 120°

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

3n3n3p0mdo98rueu33

Answer:

\(2x + 3x + 1 + 2x - 3 = 40 \\ 7x = 42 \\ x = 6\)

Answer:

D. 10

Step-by-step explanation:

To solve this question, first, find the perimeter of the triangle. Since all the sides add to 40, you can use the equation:

a + b + c = 40

Where a, b, and c are the sides.

2a - 3 + 3a + 1 + 2a = 40

Combine like terms.

2a + 3a + 2a - 3 + 1 = 40

7a - 2 = 40

Add 2 to both sides.

7a = 42

Divide both sides by 7.

a = 6

Now that you know this, find the values of each side.

Side 1:

2a - 3

2(6) - 3

12 - 3

9

Side 2:

3a + 1

3(6) + 1

18 + 1

19

Side 3:

2a

2(6)

12

This means that the longest side is side 2 (19, or 3a + 1) and the shortest side is side 1 (9, or 2a - 3).

To find how much bigger the longest side is than the shortest side, take the difference of the two sides.

19 (longest side) - 9 (shortest side) = 10.

Let a represents adult and c represents child;

On Wednesday;

Then, we substitute the value of a in the equation, we have;

26 child tickets were sold that day.

Answer:

1

Step-by-step explanation:

a fourth is 1/4 meaning Fourth = 1/4

Answer:

It would be a 2/6 chance, or a 1/3 chance.

Step-by-step explanation:

Answer:

4x+4y

Step-by-step explanation:

Answer:

2.56

Step-by-step explanation:

100%->23.86

15%-> 3.579

3.579+23.86=27.439(how much he needs to pay including tip)

30-27.439=2.561

                ≈2.56 (since we dont usually pay up to 3 d.p.)

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:

A = B + 0.2B

Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:

A = 1.2B

Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:

(B lebih kecil dari A) / A x 100%

Substitusikan nilai A = 1.2B dan kita dapatkan:

(B lebih kecil dari 1.2B) / 1.2B x 100%

Maka:

0.2B / 1.2B x 100%

= 0.1667 x 100%

= 16.67%

Jadi, B adalah 16.67% lebih kecil dari A.

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