How much bigger is 5 x 10^4 than 4 x 10^4

The cost of the labor per hour is $ 45

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The total cost of the parts is = $ 141

The total number of hours worked by the technician = 4.25 hours

The total cost of repair = $ 332.25

Let the cost of the labor be = y

The total cost of labor =
Cost of the labor per hour x Number of hours worked by the technician

The total cost of labor = 4.25y

Now ,

The total cost of repairing the computer =
Total cost of labor  + Total cost of the parts

The total cost of repairing the computer = 141 + 4.25y

332.25 = 141 + 4.25y

Subtracting 141 on both sides , we get

4.25 y = 191.25

Divide by 4.25 on both sides , we get

y = $ 45

Therefore cost of labor per hour y = $ 45

Hence , the total cost of labor per hour is $ 45

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The nth-degree polynomial that satisfies the aforementioned conditions is the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).

Given that:

p is of degree 3.

1 + 6i and -9 are zeros of p.

Since 1 + 6i is an imaginary number equal to zero so 1 - 6i must also be the one equal to zero.

So, p (x) = A (x + 9) (x - (1 + 6i)) (x- (1-6i))

p (x) = A (x + 9) (x - 1 - 6i) (x - 1 + 6i) ........ (Z)

Using formula:

(a-b) (a+b) = a² - b²

(a-b)² = a² - 2ab + b²

Assume, x - 1 = a, 6i = b  

p (x) = A (x + 9) (x² - 2x + 1 + 36)

As i² = -1

p (x) = A (x + 9) (x² - 2x + 37)

Solving this equation we get,

p (x) = A (x³ - 2x² + 37x + 9x² - 18x + 333)

p (x) = A (x³ + 7x² + 19x + 333) ....... (1)

Given that:

p(2) = -1221

Putting the value of x = 2 and p(2) = -1221 in equation (1).

p(2) = A (2³ + 7(2²) + 19(2) + 333)

=> -1221 = A (8 + 28 + 38 + 333)

=> A = -1221/407

=> A = -3

Putting the value of A = -3 in equation (Z).

Hence, the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).

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The "key" for a combination padlock involves a 210 combination.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Here, we have

A combination padlock has 10 digits to choose from for each of the

four sections of the lock.

so,  we apply a combination

¹⁰C₄ = 10! / (6! × 4!)

      = (10 × 9 × 8 × 7 × 6!) / (6! × 4!)

      =  (10 × 9 × 8 × 7)/ 4!

     = (10 × 9 × 8 × 7)/ (4 × 3 × 2 × 1)

  =  210

Hence, the "key" for a combination padlock involves a 210 combination.

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Answer: 29, 36, 38

Step-by-step explanation:

The sequence starts with 2 and proceeds to go to 9, which is a difference of 7.

After 9 it is 11, and the difference is 2.

After 11 it is 18 which is a difference of 7 again.

The pattern is difference of 7, difference of 2.

Since there was a difference of 7 between 20 and 27, the next difference will be 2, which is 29.

So, the pattern is +2, +7, +2 . . .

Therefore, your next three numbers will be 29, 36, 38

The discount rate used in calculator wound be 4.56%.

Given that,

You anticipate getting a bonus of $10000 after five years on the job.

We have the result of your calculation for the parent value of this bonus is $8000. what percentage of a discount rate did you use.

We know that to find the present value of a future sum of money .

PV= FV/(1+r)ⁿ

Here,

PV is present value = $8000

FV is future value = $10000

r is discount rate we have to find

n is time = 5 years

Substitute in the formula,

$8000=$10000/(1+r)⁵

(1+r)⁵=$10000/$8000

(1+r)⁵=1.25

1+r=[tex]1.25^{1/5}[/tex]

1+r=1.0456

r=1.0456-1

r=0.0456

r=4.56%

Therefore, The discount rate used in calculator wound be 4.56%.

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The weight of one package beef is 8.26kg

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

For example, if 10 students are to share 100 oranges, if they are to share it equal, then each students will receive 100/10= 10 oranges

Similarly 132.16kg was placed into 16packages of equal weight.

Therefore the weight of each package beef will be 132.16/16= 8.26kg

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Answer:

Step-by-step explanation:

220.5-(12.8+20.25+18.2+25.5)

220.5-(76.25)

143.75 lbs of ice left

Kyra takes 105 minutes to cover a distance of 7 miles if she walks at  a speed of 1/15 miles per minute.

Given,

Kyra is participating in a fundraiser walk-a-thon.

She walks 2 miles in 30 minutes

We have to find the time taken by Kyra to cover 7 miles if she continues the same rate of speed;

Here,

2  miles in 30 minutes

Then,

Speed = distance / time

Speed = 2 / 30

Speed = 1/15 miles per minute

Now,

The time taken to cover 7 miles;

Speed = distance / time

1/15 = 7 / t

t = 7 x 15

t = 105 minutes

That is,

Kyra takes 105 minutes to cover a distance of 7 miles if she walks at  a speed of 1/15 miles per minute.

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Supoose a<1 compared to the parent function then parabola is wider than the parent function.

An equation is an expression that shows the relationship between two or more numbers and variables.

Direction the parabola opens the value of p as positive, the parabola opens up.

The focus and vertex both have the same x position, so the distance would be in terms of the y-coordinates only.

Supoose a<1 compared to the parent function then parabola is wider than the parent function

If "a" is a fraction less than one, therefore the parabola becomes wider.

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Answer:

164 pillows

Step-by-step explanation:

Equation: 124 + 5(8)

Answer:

a) -3x + y = 8

Step-by-step explanation:

Now we have to,

→ find which of these equations is linear.

Format of linear equation,

→ Ax + By = C

Then the linear equation is,

→ Ax + By = C

→ -3x + y = 8

Hence, answer is -3x + y = 8.

Answer:

A. -3x + y = 8

Step-by-step explanation:

Definition of a Linear Equation:

This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.

This is not a linear equation as the highest power of the term in x is 2.

This is not a linear equation as the highest power of the term in x is 3.

This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.

Answer: $267,273

Step-by-step explanation:

$197,980 × 0.35 (35%) = $69,293

$197,980 + $69,293 = $267,273

Jessica now makes $267,273 annually.

A model of the given expression on a number line is represented by a number line with open circle on point negative 11 over 2 (-11/2) and arrow shaded to the left.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the information provided, we have the following mathematical expression:

x = -3 - 2 1/2

x = -3 - 5/2

x = -11/2 or -5.5.

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The sales price of the yoga pants is $20.

It should be noted that from the information illustrated, the Yoga pants are on sale for 1/3 off the original price and a pair of yoga pants normally costs $60.

The sales price will be:

= Fraction given × Original price

= 1/3 × $60

= $20

The price is $20.

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Answer:

Step-by-step explanation:

The total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.

We are given:

Rollie has a credit card limit of $4,000.

He made the following purchases: $425.36, $358.33, $377.11, and $90.20.

We need to find the total amount of purchases and Rollie's available credit card limit.

To find the total amount of purchases, we need to perform the addition that is add all the expenses:

The total amount of purchases

= addition of all purchases

= $425.36 + $358.33 + $377.11 +  $90.20

= $1251

We need to subtract the total amount of purchases from the credit card limit to get Rollie's available credit card limit.

So,

Rollie's available credit card limit

= credit card limit - the total amount of purchases

= $4000 - $1251

= $2749

Thus, the total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.

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15/4 days take 20 men to complete the task.

Given,

In the question:

The number of days worked is inversely proportional to the number of people.

If it takes 15 people to collect and pile sand for the construction of a classroom in five days.

To find the how many days take it 20 men to complete the task?

Now, According to the question:

Based on the given condition:

Formulate:

5 x 15 ÷ 20

Calculate :

5x 15/ 20

Cross out the common factor:

=15/4

Hence, 15/4 days take 20 men to complete the task.

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Answer:

39

Step-by-step explanation:

The given function to us is ,

[tex]\longrightarrow f(x) = 3x^3 + 1\\ [/tex]

We need to find the average rate of change between [tex] x=1 [/tex] and [tex] x=3[/tex] .

We can calculate the average rate of change as ,

[tex]\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} [/tex]

So that ,

[tex]\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ [/tex]

[tex]\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ [/tex]

[tex]\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\[/tex]

[tex]\longrightarrow A(x) = \dfrac{78}{2}\\ [/tex]

[tex]\longrightarrow\underline{\boxed{ A(x) = 39}} [/tex]

The Mathematical Final Answer:

0

Answer:

a>11
[tex]a\leq 8[/tex]

Step-by-step explanation:

a+3>14
 -3.  -3

   a>11
a-5<=3

 +5. +5

  a<=8

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The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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Answer: h = 46.25

Step-by-step explanation:

You can use the formula below to calculate the value of its interior angle:

       [tex]\frac{(n-2)*180}{n} =\frac{(18-2)*180}{18} =\frac{16*180}{18} =160[/tex]

So, each one of its interior angles is equal to 160°. Set that equal to the given angle measure and solve:

[tex]160=4h-25\\\\4h=160+25=185\\\\h=46.25[/tex]

Answer:

The equation in standard form of the line y=1/9x+5 is y-5=1/9(x-0)

The equation of the line in slope-intercept form is y = 5x-22.

The slope-intercept form of a straight line is one of the most common forms used to represent the equation of a line.

The slope-intercept form of an equation is given as

Formula:

Where:

Substitute these values into equation 1

Hence, the equation in slope-intercept form is y = 5x-22.

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The slope of the linear function that models this situation is given as follows:

m = 0.25.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

Hence the coefficients of the function and their meaning are obtained as follows:

In this problem, these parameters are defined as follows:

Hence the linear function modelling the situation is:

y = 8 + 0.25x.

The problem asks for what is the slope of this situation.

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The two possible locations of L are (-2,-1) and (14/3, -5/3).

According to the question,

We have the following information:

JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.

We know that the following formulas are used to find the coordinates of a point:

x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]

y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]

In this case, we have the following values:

x1 = -10 and y1 = 1

x2 = 2 and y2 = -1

m = 2 and n = 1

So, we have:

x = {2*2+1*(-10)}/(2+1)

x = (4-10)/3

x = -6/3

x = -2

For the negative sign:

x = {2*2-1*(-10)}/3

x = (4+10)/3

x = 14/3

x = 4.67

The values of y:

y = {2*(-2)+1*1}/3

y = (-4+1)/3

y = -3/3

y = -1

For the negative sign:

y = {2*(-2)-1*1}/3

y = (-4-1)/3

y = -5/3

y = -1.67

Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).

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Answer:

d. If corresponding angles are congruent, then the lines are parallel

Step-by-step explanation:

This is an example of two lines intersected by a transversal. If corresponding angles on both lines are equal, then the lines must be parallel! Think about it! If both of the two-mark angles were 30 degrees, both lines would be pointing in the exact same direction - parallel!

If corresponding angles are congruent, then the lines are parallel thus option (d) is correct.

Two lines in the same plane that are equally spaced apart and never cross each other are said two lines in the same plane that are equally spaced apart and never cross each other to be parallel lines.

As per the given two parallel lines and one transversal.

The angle with a single mark is collectively known as the corresponding angle.

If the corresponding angle is the same insure that both lines which intersect at single lines will be parallel.

Hence "If corresponding angles are congruent, then the lines are parallel".

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The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.

Kinematics is the study of the motion of an object without reference to the force that causes the motion.

The speed of the passenger train = 30 + The speed of the freight train

Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train

Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours

From kinematic equations, we get;

Speed of the passenger train = 30 + v

Distance traveled by the passenger train in 6 hours = 3 × d

(30 + v) × 6 = 3•d

6•v = d

Which gives; (30 + v) × 6 = 3 × 6•v

180 + 6•v = 18•v

12•v = 180

v = 180 ÷ 12 = 15

The speed of the freight train is v = 15 mi/hr

The speed of the passenger train = 30 + v

The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr

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