point(s) possible
Acme Movers charges $210 plus $20 per hour to move household goods across town. Hank's Movers charges $55
per hour. For what lengths of time does it cost less to hire Hank's Movers?

To convert 14 cm² to in² using dimensional analysis, we can use the following conversion factors:

1 cm = 0.393701 in (exact conversion factor)

1 in = 2.54 cm (exact conversion factor)

We want to convert cm² to in², so we need to use the conversion factor that relates cm² to in². This is:

1 cm² = (0.393701 in)² = 0.15500031 in² (approximate conversion factor)

To set up the dimensional analysis, we start with the given quantity and multiply it by the appropriate conversion factors so that the units cancel out and we are left with the desired units. We can set it up as follows:

14 cm² * (0.15500031 in² / 1 cm²) = 2.17000434 in² (approximate answer)

Therefore, 14 cm² is approximately equal to 2.17000434 in².

Answer:

13.44

Step-by-step explanation: tax is added after payment so 12 + 5% or 100% + 12% = 112% of 12. There are many ways to solve for this, I used number line starting out because it was easiest for me, just divide 12 by 100 and put that into 1% then multiply that 1% number by 112 and you get 112%.

Answer:

Hello!!

The cost of a $12 t-shirt with 5% tax would be...

$12.60

Step-by-step explanation:

\(12\) × \(0.05=0.6\)

\($12 + 0.6=12.60\)

Hope this helps!!

Answer:

The coordinates of the dillated vertices are \(A'(x,y) = (2,2)\), \(B'(x,y) = (4,4)\), \(C'(x,y) = (8,2)\) and \(D'(x,y) = (4,-2)\).

Step-by-step explanation:

From Linear Algebra, we define dilation by the following equation:

\(P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]\) (1)

Where:

\(O(x,y)\) - Center of dilation, dimensionless.

\(P(x,y)\) - Original point, dimensionless.

\(k\) - Scale factor, dimensionless.

\(P'(x,y)\) - Dilated point, dimensionless.

If we know that \(O(x,y) = (0, 0)\), \(k = 2\), \(A(x,y) = (1,1)\), \(B(x,y) = (2,2)\), \(C(x,y) = (4,1)\) and \(D(x,y) = (2,-1)\), then the dilated points are, respectively:

Point A

\(A'(x,y) = O(x,y) + k\cdot [A(x,y)-O(x,y)]\) (2)

\(A'(x,y) = (0,0) + 2\cdot [(1,1)-(0,0)]\)

\(A'(x,y) = (2,2)\)

Point B

\(B'(x,y) = O(x,y) + k\cdot [B(x,y)-O(x,y)]\) (3)

\(B'(x,y) = (0,0) + 2\cdot [(2,2)-(0,0)]\)

\(B'(x,y) = (4,4)\)

Point C

\(C'(x,y) = O(x,y) + k\cdot [C(x,y)-O(x,y)]\)

\(C'(x,y) = (0,0) + 2\cdot [(4,1)-(0,0)]\)

\(C'(x,y) = (8,2)\)

Point D

\(D'(x,y) = O(x,y) + k\cdot [D(x,y)-O(x,y)]\)

\(D'(x,y) = (0,0) + 2\cdot [(2,-1)-(0,0)]\)

\(D'(x,y) = (4,-2)\)

The coordinates of the dillated vertices are \(A'(x,y) = (2,2)\), \(B'(x,y) = (4,4)\), \(C'(x,y) = (8,2)\) and \(D'(x,y) = (4,-2)\).

The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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Solve for x

We can use sine

Answer:

The equation of a line tells us both the y-intercept and the slope of a line on a graph. The equation of a line that passes through the points (2, -4) and (6, 10) is:

\(y=\frac{7}{2}x(3.5)-11\)

Step-by-step explanation:

Two points of the line are (2, -4) and (6, 10).

The equation of the line using two ordered pairs (points/coordinates).

The equation of a line with a known/revealed slope (m - variable used) can come in the format of:

y = mx + b

Using this information, we can use the formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\) (To find the slope/constant of variation/gradient/rate of change) - all synonyms; used for different contexts.

Now using the points, let's plug them into the formula and solve:

\(m=\frac{10-(-4)}{6-2}\)

\(m=\frac{14}{4}\)

\(m=\frac{7}{2} (\text{Decimal form:} 3.5)\)

Now that we have found the slope, let's find the equation of the line.

Let's use the formula: \((y-y_1)=m(x-x_1)\)

⇒ Now let's plug in and solve:

       ⇒ \([y-(-4)]=\frac{7}{2} (x-2)\)

      ⇒ \(y+4=\frac{7}{2} x-7\)

   ⇒ \(y=\frac{7}{2} x-7-4\)

  ⇒ \(y=\frac{7}{2} x-11\)

Now that we have found the equation of the line, we have completed the question as we have it now answered.

Hence, the equation of the line with the points of (2, -4) and (6,10) is

y = 7/2x - 11

(Keep in mind: This format is known as the slope-intercept form.)

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Answer:

Step-by-step explanation:

Its the closed dot on 9. i just did the quiz. Your welcome.

Answer: the closed dots on 9 10 11 12 13 14

15

Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375

What do you mean by capital?

Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.

A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.

Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375

So, Total assets= £10,375

Payable=  £1,600, loan from Rub= £2,500, Balancing figure= £6,275

Total liabilities= £10,375

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Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Answer: 400

Step-by-step explanation:

The total estimated number of retirees at the senior center in retirement community in Florida in March  is 1,740.

To estimate the total number of retirees at the senior center in March, round each weekly attendance to the nearest tens place and add them together:

To the nearest tens, we have

First week: 346 ≈ 350

Second week: 412 ≈ 410

Third week: 293 ≈ 290

Fourth week: 689 ≈ 690

Add the estimated values

350 + 410 + 290 + 690

= 1,740

Therefore, the total estimated number of retirees at the senior center in March is 1,740.

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

Answer:

d

Step-by-step explanation:

1 kg has 1000 g

Then 2,5 kg has 2,5 × 1000 = 2500 g

You can also make a proportion:

1 kg - 1000 g

2,5 kg - x g

Use the property of the proportion to find x (cross-multiply):

x = 2,5 × 1000 / 1 = 2500 g

Answer: (compiled from google)

One radian is the measure of the central angle of a circle such that the length of the arc is equal to the radius of the circle.

A full revolution of a circle ( 360 ∘ ) equals  2 π   r a di a n s. This means that  1  radian = 180 ∘ π .  

The formula used to convert between radians and degrees is  angle in degrees = angle in radians ⋅ 180∘ π .

The radian measure of an angle is the ratio of the length of the arc to the radius of the circle  ( θ = sr ) . In other words, if  s  is the length of an arc of a circle, and  r  is the radius of the circle, then the central angle containing that arc measures radians.

Key Terms

arc: A continuous part of the circumference of a circle.

circumference: The length of a line that bounds a circle.

radian: The standard unit used to measure angles in mathematics. The measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle.

The  x – and  y -coordinates at a point on the unit circle given by an angle  

t  are defined by the functions  x = cos t  and  y = sin t .

Although the tangent function is not indicated by the unit circle, we can apply the formula  

tan  t = sin  t  cos  t  to find the tangent of any angle identified.

Using the unit circle, we are able to apply trigonometric functions to any angle, including those greater than  90 ∘ .

The unit circle demonstrates the periodicity of trigonometric functions by showing that they result in a repeated set of values at regular intervals.

Key Terms

periodicity: The quality of a function with a repeated set of values at regular intervals.

unit circle: A circle centered at the origin with radius 1.

quadrants: The four quarters of a coordinate plane, formed by the  x – and y -axes.

If this doesn't help I appologize

Answer:the variable k is the constant of proportionality

Step-by-step explanation:

This can be proven when the equation is used to find different values of y. To find these different values, the x variable is substituted for different values while the k value stays the same. hope this helps!!

Step-by-step explanation:

Let x be the height of the tree. The length of shadow of tree is l=20 feet and elevation of sun is θ=400.

Then, tanθ=xlortan40=x20orx=20tan40=16.78(2dp)feet

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Answer:

62.9 ft (nearest tenth)

Step-by-step explanation:

Use the tan trig ratio to calculate the length of the shadow.

Tan trigonometric ratio

\(\sf \tan(\theta)=\dfrac{O}{A}\)

where:

Let x = length of shadow

Given:

Substitute the given values into the formula and solve for x:

\(\implies \sf \tan(50^{\circ})=\dfrac{75}{x}\)

\(\implies \sf x=\dfrac{75}{\tan(50^{\circ})}\)

\(\implies \sf x=62.93247234...\)

Therefore, the length of the shadow is 62.9 ft (nearest tenth)

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

pay phone:

distance call

Step 02:

equations:

3 minutes:

$0.95

$0.12 per additional minute

x = # additional minutes

$5.00 = $0.95 + $0.12x

5 = 0.95 + 0.12x

5 - 0.95 = 0.12x

4.05 = 0.12x

4.05 / 0.12 = x

33.75 = x

total minutes = 3 min + 33.75 min = 36.75 min

The answer is:

total minutes = 36.75 min

Answer:

28 MEN

Step-by-step explanation:

X + X-3=59

2X-3=59

2X=62

X=31

MEN=31-3=28

Answer:

Step-by-step explanation:

0.033

Answer:

1.

90+27

2.

90 = 9 x 10

3.

27 = 9 x 3

4.

So apply the distributive property would be:

90 + 27 = 9(10 + 3)

Step-by-step explanation:

Answer:

The greatest common factor of 90 and 27 is 9.

Using the distributive property , you could write: 9(10 + 3)

here, on solving  company reduced the size of their percentage  container of dishwashing soap to 4.5 ounces from its original 5 ounce capacity.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

The initial size was x.

Since 100% - 10% = 90%, 0.9x is 10% smaller than the original size.

90% of the original size is equal to 4.5 ounces,

hence the calculation we use to determine the original size x is:

0.9 x = 4.5 x

= 4.5 / 0. 9 x = 5

The bottle's initial capacity was 5 ounces.

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Answer:

Answer: {b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}

Step-by-step explanation:

A' = U-A

={b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}

Answer:

\(x\leq6\text{ or } x>30\)

Step-by-step explanation:

We are given the compound inequality:

\(\displaystyle 9x+4\leq 58\text{ or } \frac{1}{6}x-2>3\)

Note that this is an "or" inequality. In other words, we just have to solve each inequality individually and then combine the answers!

1)

We have:

\(9x+4\leq58\)

Subtract 4 from both sides:

\(9x\leq54\)

Divide both sides by 9:

\(x\leq6\)

So, our first solution is all numbers less than or equal to 6.

2)

We have:

\(\displaystyle \frac{1}{6}x-2>3\)

Add 2 to both sides:

\(\displaystyle \frac{1}{6}x>5\)

To cancel out the fraction, let's multiply both sides by 6. So:

\(\displaystyle 6\left(\frac{1}{6}x\right)>6(5)\)

The left side will cancel. Therefore:

\(x>30\)

So, our second solution is all numbers greater than 30.

Therefore, our full solution will be:

\(x\leq6\text{ or } x>30\)

And we're done!

Answer:

−8x−7y=96 (* 5)

−3x+5y=−25  (* 7)

-40x - 35y = 480

-21x + 35y = -175

=> -61x = 305

x = -305/61

x = -5

-3x + 5y = -25  

-3 * (-5) + 5y = -25

5y = -40

y = -8 =>

x = -5

y = -8

9x+4≤58 or 16x−2>3

9x ≤ 54 or 16x > 5

x ≤ 6 or x > 5/16

Answer:

Step-by-step explaination

First you want to make a percent porportion so that you can find the unknown value. 135 = 25% Solve it and you'll get your answer.

                           ?     = 100%

Answer:

y = 1

Step-by-step explanation:

Given

⇒ y = kx⁴

Finding the proportionality constant, k

Finding y

Answer: 18.18%

Step-by-step explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

\($$SA = 2lw + 2lh + 2wh$$\)

where \(\(l\)\) is the length, \(\(l\)\) is the width, and \(\(h\)\) is the height. For the original piece of wood, \(\(l = 10\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\).

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, \(\(l = 5\) inches\), \(\(w = 4\) inches\), and \(\(h = 5\) inches\). The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

\($$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$\)

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.