You want to produce a scale drawing of your living room. Which is 24 ft by 27 ft. If you Use a scale of 2 inches.= 3ft what will be the dimensions of your scale drawing ?
A) 16in. By 18in.
B) 6in. By 18in
C) 6in. By 72 in
D) 16 in by 72 in

Answer:

➨ f(-1) = 0

Step-by-step explanation:

➨ Look at the table and compare.

Notice that when x = -1, f(x) = 0

f(-1) is like substituting x = -1 and get the f(x) value at x = -1.

Thus, f(-1) = 0

Answer: 27 x 1/3

Step-by-step explanation: 27/1 x 1/3 = 9 orchards per store

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

John manages 27 apple orchards in North Georgia. He wants to split the orchards into thirds so that he can open 3 local stores.

Then the number of orchards in each store will be

⇒ 27 / 3

Then the expression can be written as,

⇒ 27 x (1/3)

The number of orchards in each store will be 27 x (1/3). Then the correct option is A.

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Answer:

6 - 6r

Step-by-step explanation:

we just plug in 3r - 1 instead of x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= 6 - 6r

Given :-

To Find :-

Solution :-

Here since the slope of the line is 7 and y intercept is -7 , we can use the slope intercept form of the line to find the equation of the line . The slope intercept form of the line is ,

\(\longrightarrow\) y = mx + c

On putting the respective values ,

\(\longrightarrow\) y = 7(x) + (-7)

\(\longrightarrow\) y = 7x - 7

For the graph see attachment .

Let initial bacteria, P0=10000.

A colony of 10,000 bacteria doubles in size every 29 hours.

So, in first 29 hours, the bacteria becomes 20000.

In the next 29 hours, the bacteria becomes 40000.

Now, 29+29=58 hours.

In the next 29 hours, the bacteria becomes

Now, the total hours is 58+29=87 hours.

So, in 87 hours the bacteria becomes 80000.

The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

\(V = \frac{4\pi r^3}{3}\)

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

The sphere is given by the image presented at the end of the answer.

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Answer:

I'll try my best in explaining the steps.

Considering both signs are greater than and less than sign, its an open circle.

For the first equation, you would have an open circle, basically one that isn't colored in, on 8 on the number line. The arrow would be pointing to the left because the equation is telling us numbers that are less than 8.

For the second equation, you would have an open circle, basically one that isn't colored in, on -1 on the number line. The arrow would be pointing to the right because the equation is telling us numbers that are greater than -1.

Step-by-step explanation:

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

9/10

Step-by-step explanation:

combine the fractions yk?

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Answer:

The balance in the account after 3 years is approximately $2313.94.

Step-by-step explanation:

The formula for calculating the balance in a continuously compounded account is:

B = Pe^(rt)

Where:

B = balance

P = principal

e = Euler's number (approximately 2.71828)

r = annual interest rate (as a decimal)

t = time in years

Using the given values, we have:

P = $2000

r = 0.051 (5.1% expressed as a decimal)

t = 3

Plugging these values into the formula, we get:

B = 2000e^(0.051*3)

B = 2000e^(0.153)

B = $2313.94 (rounded to the nearest cent)

Therefore, the balance in the account after 3 years is approximately $2313.94.

The proportion of people who walk more than 5 minutes to class is approximately 0.9938 or 99.38%.

To find the proportion of people who walk more than 5 minutes to class, we need to calculate the z-score for 5 minutes and then find the area under the normal distribution curve for values greater than that z-score.

The z-score can be calculated using the formula:

z = (x - μ) / σ,

where x is the value (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (2 minutes).

Substituting the values into the formula:

z = (5 - 10) / 2 = -5 / 2 = -2.5.

Next, we need to find the area under the normal distribution curve for z > -2.5. By referring to a standard normal distribution table or using statistical software, we can find that the area to the right of -2.5 is approximately 0.9938.

Therefore, the proportion of people who walk more than 5 minutes to class is approximately 0.9938 or 99.38%.

Note: It's important to note that the calculation assumes a normal distribution and that the survey accurately represents the population of GCU students.

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Answer:

Step-by-step explanation:

Its 1/3 just put that it will be right I promise

Answer:

1 Hour and 8 Minutes (If she left at 9:13 AM)

13 hours and 8 Minutes (If she left at 9:13 PM)

Step-by-step explanation:

You can figure this out by simply starting out with 8:05 AM and adding an hour to it. That starts you off with 9:05. From there you can count the remainder of the 8 minutes and use it to get your answer, 1 hour and 8 Minutes.

(For the unlikely chance she left her house at 9:13 pm, you do the same thing but instead of adding one hour you add 12, and then add the 1 hour and 8 minutes to get your answer of 13 hours and 8 minutes.)

Answer:

x = 210

Step-by-step explanation:

15 * 14 = 210

To find the corresponding point on the unit circle for the radian measure 0=5pi/6, we can use the following steps:

Recall that the unit circle is a circle with radius 1 centered at the origin of the Cartesian plane.

The radian measure of an angle in standard position (with initial side on the positive x-axis) is the length of the corresponding arc on the unit circle.

To find the point on the unit circle corresponding to 0=5pi/6, we start at the point (1,0) on the positive x-axis and move counterclockwise along the circle by an angle of 5pi/6 radians.

One way to do this is to divide the circle into 12 equal parts (since 2pi/12 = pi/6), and then count 5 of these parts counterclockwise from the positive x-axis. This brings us to the point on the circle where the angle measures 5pi/6.

This point has coordinates (-√(3)/2, 1/2) on the unit circle.

Therefore, the corresponding point on the unit circle for the radian measure 0=5pi/6 is (-√(3)/2, 1/2).

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Answer:

Primero, la formula de Herón dice que:

Para un triangulo de lados a, b, y c

\(area = \sqrt{s*(s - a)*(s - b)*(s - c)}\)

Tal que:

s = (a + b + c)/2

Y el teorema de Pitágoras dice que, para un triángulo rectángulo con hipotenusa H, y catetos A y B, se cumple que:

A^2 + B^2 = H^2

1)

a) Para un triangulo equilátero de 8 cm de lado, tenemos:

a = b = c = 8 cm

reemplazando eso en la ecuacion de s, obtenemos:

s = (3*8cm)/2 = 12cm

Ahora, remplazando s en la ecuacion del area, obtenemos:

\(area = \sqrt{12cm*(12cm - 8cm)*(12cm - 8cm)*(12cm - 8cm)} = 27.7 cm^2\)

b) Podemos dividir al triángulo equilátero en dos triángulos rectángulos, tal que:

Cada uno de esos triángulos rectángulos tiene una hipotenusa de 8 cm.

Cada uno de esos triángulos rectángulos tiene un cateto que es la mitad del largo original de la base, es decir, 8cm/2 = 4cm

Y ambos triángulos comparten un cateto, que es h, la altura del triángulo.

Usando el teorema de Pitágoras, tenemos que:

h^2 + (4cm)^2 = (8cm)^2

Resolviendo esto para h, obtenemos:

h = √( (8cm)^2 - (4cm)^2) = 6.93 cm

Ahora que conocemos la altura del triángulo, la podemos reemplazar en la ecuación del área:

area = b*h/2 = base*altura/2

y sabemos que la base del triángulo equilátero es 8cm, entonces:

area = 8cm*6.93 cm/2 = 27.72cm^2

(El resultado es un poco diferente, pero se debe principalmente a errores de redondeo)

Si redondeamos esta area a una cifra significativa, obtenemos:

area = 27.7 cm^2

2) Problema similar, esta vez tenemos un triángulo equilátero de lado 12cm.

a) a =  b = c = 12cm

s = (3*12cm)/2 = 3*6cm = 18cm

Reemplazando esto en la fórmula del área, obtenemos:

\(area = \sqrt{18cm*(18cm - 12cm)*(18cm - 12cm)*(18cm - 12cm)} = 62.35cm^2\)

b) Ahora usando teorema de Pitágoras:

De vuelta, dividimos el triángulo equilátero en dos triángulos rectángulos.

Ambos tienen una hipotenusa de 12cm

ambos tienen un cateto de 12cm/2 = 6cm

Ambos comparten un cateto que llamaremos h, que es la altura del triángulo.

Ahora aplicamos el teorema de Pitágoras:

(6cm)^2 + h^2 = (12cm)^2

Resolviendo esto para h obtenemos:

h = √( (12cm)^2 - (6cm)^2) = 10.39 cm

Ahora reemplazando esto en la ecuación del área, (recordar que la base de un triángulo equilátero de 12 cm de lado, es 12 cm)

area = b*h/2 = 12cm*10.39 cm/2 = 62.34 cm^2

De vuelta los resultados son equivalentes a una cifra significativa, y podemos asumir que la diferencia se debe, de vuelta, a errores de redondeo.

Answer: -5/6

Step-by-step explanation: 53/6= 8 5/6 -5/6=8

Answer:

d² - 24d + c = (d - 12)² - 144 + c

If you purchase dictionaries from Barker's Books rather than Sunshine Bookstore, you will receive each one for $0.50 less.

The total cost of a carton of 16 dictionaries at Sunshine Bookstore is $468, so the cost of each dictionary is:

$468 ÷ 16 = $29.25 per dictionary

At Barker's Books, the same dictionaries cost $28.75 each.

To find out how much money you will save on each dictionary if you buy them at Barker's Books, you need to subtract the cost of each dictionary at Barker's Books from the cost of each dictionary at Sunshine Bookstore:

$29.25 - $28.75 = $0.50

Therefore, you will save $0.50 on each dictionary if you buy them at Barker's Books instead of Sunshine Bookstore.

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Answer:

30 ants are in the ant farm.

---------------------------------------

If there are 40 ants on the second part of the scale,

multiply 5 by 8 to get 40 because there are 5 ants for each row, and 8 rows total

and there are 10 ants visible on the first side of the scale, the second part of the scale would have the majority and there would be a big inbalance. To fix that, we could say there are 30 ants in the ant farm, because there are 10 ants on the scale. \(10 + 30 = 40\), so that would make the scale balanced.

Answer:

The reciprocal of mixed number is 6/11

Answer:

Step-by-step explanation:

\(\frac{2017^4 - 2016^4}{2017^2 + 2016^2}\)

\(= \frac{(2017^2 - 2016^2)(2017^2 + 2016^2)}{2017^2 + 2016^2}\)

\(= (2017^2 - 2016^2)\)

\(= (2017 - 2016)(2017 + 2016)\\= 4033\)

Answer: the mean is 1.03

Step-by-step explanation: you multiple the days by the probability, 0 x .68= 0 1 x .05=.05 2 x .07=.14 and so on and you add what you get from multiplying them.

If greenfield company has a piece of manufacturing equipment with a book value of $40,000 and a remaining useful life of four years.  the total increase or decrease in income by replacing the current equipment with the new equipment is:$22,000 decrease.

Here, we have,

to find the increase or decrease in income

Annual Savings $76,000

($19,000 × 4 years)

Add Proceeds from Sale of Machine $22,000

Total  $98,000

Total increase or decrease in income = $98,000 - $120,000

Total increase or decrease in income = $22,000 (Decrease)

Therefore the decrease in income is $22,000.

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complete question:

granfield company has a piece of manufacturing equipment with a book value of $40,000 and a remaining useful life of four years. at the end of the four years the equipment will have a zero-salvage value. granfield can purchase new equipment for $120,000 and receive $22,000 in return for trading in its current equipment. the current equipment has variable manufacturing costs of $39,000 per year. the new equipment will reduce variable manufacturing costs by $19,000 per year over its four-year life. the total increase or decrease in income by replacing the current equipment with the new equipment is: