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Architects often create scale models before the actual building is constructed.
If a scale model has a length of 24 inches and a width of 36 inches, which dimensions are geometrically similar to the model building ?

Building A: 223 feet by 360 feet
Building C: 288 feet by 432 feet
Building D: 364 feet by 576 feet
Building B: 120 feet by 190 feet

Answer:

The amount which real estate agency gets is $  21,010  .

Step-by-step explanation:

Given as :

The selling price for a house = $ 382,000

The commission rate for real estate agency = 5.5 %

The commission rate for the agent = 30 %

So, the commission which real estate agency get = 5.5 % of $ 382,000

I.e the commission which real estate agency get = 0.055 × $ 382,000

Or, the commission which real estate agency get = $ 21,010

Again ,

The commission which agent get = 30 % of $ 382,000

I.e the commission which agent get = 0.3 × $ 382,000

Or, the commission which agent get = $ 114,600

Hence The amount which real estate agency gets is $  21,010  . answer

The agent earns a commission of $6,303 from the $382,000 house sale. This is calculated by first determining the real estate agency's commission of 5.5% on the sale price, which is $21,010. Then calculating 30% of this figure, which is the agent's earnings.

To calculate the total commission the agent will receive, you first have to calculate how much the real estate agency gets, and then calculate the agent's earnings based on that number.

The real estate agency's commission is 5.5% of the total sold price of the house. This can be calculated as:

(5.5 / 100) * $382,000 = $21,010

The agent then receives 30% of this amount, which you calculate as:

(30 / 100) * $21,010 = $6,303

Therefore, the agent earns a commission of $6,303 from the sale of the house.

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Answer:

6

Step-by-step explanation:

Because you have to added than reverse the question than it will give you your answer backwards

[tex](fog)(x) = -x[/tex]

Step-by-step explanation:

The composition is calculated by putting the other function in place of variable

Given

[tex]f(x) = x - 1\\g(x) = -x+1[/tex]

The composition will be:

[tex](fog)(x) = g(x) -1\\=(-x+1) -1\\=-x+1-1\\=-x[/tex]

Hence,

[tex](fog)(x) = -x[/tex]

Keywords: Composition, Functions

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Answer:

x=60.4

Step-by-step explanation:

Add 7.6 on both sides

1/4x=15.1

Multiply both sides by 4

x= 60.4

Answer:

[tex]log_{b}(b^{x r}) [/tex]

Step-by-step explanation:

A picture of the question is shown in the figure attached. There we can see that the step corresponding to Properties of exponents is the option:

[tex]log_{b}(b^{x r}) [/tex]

which is equivalent to

[tex]log_{b}((b^{x})^{r}) [/tex]

This question is based on the property of exponents.Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

Given that :

[tex]\bold{log_a(M^r)}[/tex]

In this question, we have choose appropriate correct option for for given expression.

According to the question,

It is given that,

[tex]\bold{log_a(M^r)}[/tex]                                                                                            ...(1)

Now, substitute the value of M = [tex]\bold{b^{x}}[/tex]. We get,

Thus, [tex]\bold{log_a(M^r)} = \bold{log _a((b^{x})^r)}[/tex]                                                            ...(2)

As we know that, by using the property of exponents,

[tex]\bold{(x^{m})^n = x ^{mn}}[/tex]

Now, applying this property in expression (2).

We get,

[tex]\bold{log _a((b^{x})^r)} = \bold{log _a(b^{x r})}[/tex]

Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].

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Answer:

The total miles driven equation is [tex]y=27x[/tex]

Step-by-step explanation:

Given:

Number of gallons of gas is x.

Total miles driven is y.

Carl's new car gets 27 miles per gallon.

Hence to calculate total miles driven we need to multiply 27 with number of gallons of gas.

Hence the equation becomes.

[tex]y=27x[/tex]

Answer:

Option(D)

Finger Painting can be hard for children to control, but helps free their tension

Explanation:

Finger painting is a form of art in which the paintings or drawings are created by using fingers instead of a pen, pencil or brush.In this the fingers are dipped in paint and then the drawings are made by using bare hands.

This is a hard technique to make a painting or illustration and hence can be hard for children to control, but since it involves sensing touch, it helps release the tension and soothe the mind of the person who does painting using this method.

Answer:

See step-by-step explanation

Step-by-step explanation:

Whole numbers are [tex]0,\ 1,\ 2,\ 3,\ 4,\ ...[/tex]

Integer but not whole numbers are [tex]...,\ -4,\ -3,\ -2,\ -1[/tex]

Rational numbers are fractions

Irrational numbers are numbers that are not rational

[tex]\pi[/tex] is irrational number

[tex]-100[/tex] is integer but not whole number

[tex]-34[/tex] is integer but not whole number

[tex]-4[/tex] is integer but not whole number

[tex]-\dfrac{8}{4} =-2[/tex] is integer but not whole number

[tex]0.333...=\dfrac{1}{3}[/tex] is rational number

[tex]0.456783...[/tex]  is irrational number

[tex]3[/tex] is whole number

[tex]9.23456=\dfrac{923,456}{100,000}[/tex] is rational number

[tex]\sqrt{4}=2[/tex] is whole number

[tex]\sqrt{8}=2\sqrt{2}[/tex] is irrational number

[tex]\dfrac{1}{2}[/tex] is rational number

[tex]\dfrac{49}{7}=7[/tex] is whole number

[tex]\dfrac{89}{10}[/tex] is rational number

[tex]zero[/tex] is whole number

Answer:

15

Step-by-step explanation:

Answer:

3*5

Step-by-step explanation:

GCF of 45 and 75 = 15

15: 1,3,5,15

3 and 5 are prime numbers so: 3*5=15

Answer:

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is [tex]\frac{1}{8}[/tex] x

∠4 and ∠6 are same side interior angles and are supplementary, thus

x + [tex]\frac{1}{8}[/tex]x = 180

Multiply through by 8 to clear the fraction

8x + x = 1440, that is

9x = 1440 ( divide both sides by 9 )

x = 160

Hence ∠4 = 160° and ∠6 = 160° ÷ 8 = 20°

Answer:

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

Step-by-step explanation:

From the graph, we can say that

[tex]m \angle 6 + m \angle 4 = 180 \°[/tex]

Because they are consecutive interior angles, and they sum 180° by definition. So, the reason of third statement is "by definition of consecutive interior angles".

We already know that

[tex]m \angle 6 = \frac{1}{8} \times m \angle 4[/tex]

But,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 = 180\° - m \angle 4[/tex]

Replacing this, we have

[tex]180\° - m \angle 4=\frac{1}{8}(m \angle 4)\\(\frac{1}{8}+1) (m\angle 4)=180\°\\\frac{9}{8}(m\angle 4) = 180 \°\\ m \angle 4 = \frac{180(8)}{9}= 160\°[/tex]

Then,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 + 160\° =180\°\\m \angle 6 = 180-160=20[/tex]

Therefore, the measures of these two angles are

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

Answer:

2x-5

Step-by-step explanation:

(4x-7)-(2x-2)=4x-2x-7-(-2)=2x-7+2=2x-5

Answer:

2x-5

Step-by-step explanation:

Answer:13 hours

Step-by-step explanation:

So you would divide 737 (miles) by 11 (hours) in order to find how far he traveled in 1 hour. You should get 67. So he travels at 67 miles in 1 hour. Then you would divide 871(total miles) by 67(distance traveled in 1 hour) to find out how many hours it took to travel 871. You should get 13(hours).

Hoped it helped.

The area of pasture is 60000 square feet.

Step-by-step explanation:

Perimeter of rectangular pasture = 1000 feet

Width of pasture = w

Length of pasture = l = w+100

We know that,

Perimeter = 2(Length+width)

[tex]1000=2(w+100+w)\\1000=2(2w+100)\\1000=4w+200\\1000-200=4w\\800=4w\\4w=800[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{800}{4}\\w=200[/tex]

Width is 200 feet.

Length = w+100 = 200+100 = 300 feet

Area of pasture = A = Length * Width

[tex]Area\ of\ pasture=300*200\\Area\ of\ pasture=60000 \ ft^2[/tex]

The area of pasture is 60000 square feet.

Keywords: rectangle, area

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The question is about calculating the area of a rectangular pasture given its perimeter and relation between its length and width. After setting up equations based on the given conditions and calculating, the area of the pasture is found to be 60,000 square feet.

The subject of this question is Mathematics, specifically dealing with the calculation of area from given perimeter and length-width relationship in a rectangle. Let's denote the width of the rectangular pasture as 'w', and its length would then be 'w+100'.

The formula for the perimeter of a rectangle is 2*(length + width). As given, the perimeter is 1000 feet, so we set up the equation: 1000 = 2*(w+100 + w).

Simplify this to get the width 'w' which is 200 feet and the length is 'w+100', so 300 feet.

The area of a rectangle is calculated by the formula length*width, therefore, calculating gives 200*300 = 60,000 square feet.

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Step-by-step explanation:

[tex](6i)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=6^3i^3\\\\\text{If}\ i=\sqrt{-1},\ \text{then}\\\\6^3i^3=216(-i)=-216i\\\\\text{else}\\\\6^3i^3=216i^3[/tex]

Final answer:

The expression equivalent to (6i)^3 is -216i, achieved by cubing the digit 6 to get 216 and remembering that i^3 is -i.

Explanation:

To find an expression equivalent to (6i)^3, we follow the rules of exponentiation and imaginary numbers. First, we cube the digit part, which is 6, to get 6^3 = 216. Next, we cube the imaginary unit i. Recall that i is the imaginary unit where i^2 = -1. Thus, i^3 is the same as i^2 multiplied by i, which equals to -i.

Combining these, we obtain (6i)^3 = 6^3 * i^3 = 216 * (-i) = -216i. This is the simplified form of the original expression.

Answer: 729

Step-by-step explanation: 1st term X common ratio(desired term-1)

The 7th term in the sequence is -2187.

To find the 7th term in the sequence 1, -3, 9, -27, ..., we can observe that each term is obtained by multiplying the previous term by -3. Therefore, to find the 7th term, we start with the first term 1 and repeatedly multiply by -3:

So, the 7th term in the sequence is -2187.

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Answer:

Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minutes.

Step-by-step explanation:

Tanya walked 15 laps on an indoor track in 30 minutes.

Therefore, the average speed of Tanya is [tex]\frac{15}{30} = \frac{1}{2}[/tex] laps per minutes.

Calculation:

The average speed formula is given by [tex] V = \frac{\textrm {Distance covered}}{\textrm {Number of munutes spent}}[/tex]

The distance is 15 laps.

The time is 30 minutes.

Therefore, [tex]V = \frac{15}{30}[/tex] laps per minute.

After simplification, [tex]V = \frac{1}{2}[/tex] laps per mins.

Therefore, Tanya's average speed was [tex]\frac{1}{2}[/tex] laps per minute. (Answer)

Answer:

19??

Step-by-step explanation:

Answer:

yes it is 19 all you have to do is add 12 and 7

5/7 x 7/3

Multiply the numerators together and the denominators:

(5 x 7) / (7 x 3)

35/21 reduces to 5/3 = 1 2/3

Answer:

The height is 1343.13 meters.

Step-by-step explanation:

Air pressure may be represented as a function of height h in meters above the surface of Earth as shown below :

[tex]P(h) = P. e^{-0.000121h}[/tex] ......... (1)

In this function, P is air pressure at sea level and h is measured in meters.

Let at a height of h meters the pressure is 85% of the sea level pressure.  

Hence, from equation (1), we get

[tex]0.85 = e^{- 0.000121 h}[/tex]

Taking ln both sides, we can write

ln 0.85 = -0.000121 h (ln e) {Since [tex]\ln a^{b} = b \ln a[/tex]}

⇒ h = 1343.13 meters (Answer)

Answer:The formula for variable h can be calculated by the following steps;

Step-by-step explanation:

f=8gh

f/8g=h

Or

h=f/8g

To solve for the variable h in the formula f = 8gh, divide both sides of the equation by 8g. The formula for the variable h is h = f / (8g).

To solve the formula for the variable h, we need to isolate h on one side of the equation. In this case, the equation is f = 8gh. To isolate h, we divide both sides of the equation by 8g. This gives us:

h = f / (8g)

So the formula for the variable h is h = f / (8g).

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Answer:

75% decrease

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = [tex]\frac{2}{5}[/tex] x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y =  [tex]\frac{5}{2}[/tex] x + [tex]\frac{6}{2}[/tex]

I.e y =  [tex]\frac{5}{2}[/tex] x + 3

So,  slope of this line = [tex]m_1[/tex] =  [tex]\frac{5}{2}[/tex]

Again , From Line 2

y = [tex]\frac{2}{5}[/tex] x - 1

So, slope of this line =  [tex]m_2[/tex] =  [tex]\frac{2}{5}[/tex]

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - [tex]\frac{6}{4}[/tex] -  [tex]\frac{10}{4}[/tex] x

I.e y =  - [tex]\frac{5}{2}[/tex] x  - [tex]\frac{6}{4}[/tex]

So, Slope of this line = [tex]m_3[/tex] = - [tex]\frac{5}{2}[/tex]

Now, If the lines are parallel , then the slope of the lines are equal

And  If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

[tex]m_2[/tex] × [tex]m_3[/tex] = [tex]\frac{2}{5}[/tex] × ( - [tex]\frac{5}{2}[/tex] )

I.e [tex]m_2[/tex] × [tex]m_3[/tex] = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Answer

To complete the pairs and have a difference of 3, add 4 to both sides of the equation.

To complete the pairs and have a difference of 3, the first number of the pair should be the larger number.

So, the equation ? - 4 = 3 can be solved by adding 4 to both sides of the equation.

? - 4 + 4 = 3 + 4

? = 7

Answer: The value of x is 40

Step-by-step explanation:

Given triangle SRT,

Angle SRT = 20 and Angle SRT = Angle STR

To find Angle STU:

We know that

The sum of all interior angles of triangle is equal to 180.

Angle SRT + Angle STR + Angle RST =180

Also, Angle SRT = Angle STR =20

20+20+Angle RST=180

Angle RST=140.

Now. The exterior angle of triangle is equal to sum of opposite interior angles of triangle,

Angle STU=4x=Angle RST+Angle SRT

4x=20+140

4x=160

x=40

Therefore, The value of x is 40

Answer: 19.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}\\\\\text{Calculate what fraction of 30 is 18 and convert it to percent:}\\\\\dfrac{18}{30}=\dfrac{18:6}{30:6}=\dfrac{3}{5}\\\\\dfrac{3}{5}\cdot100\%=\dfrac{300}{5}\%=60\%[/tex]

[tex]\bold{METHOD\ 2:}\\\\\begin{array}{ccc}30&-&100\%\\\\18&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\(30)(p)=(18)(100)\\\\30p=1800\qquad\text{divide both sides by 30}\\\\\dfrac{30p}{30}=\dfrac{1800}{30}\\\\p=60[/tex]

Final answer:

18 is 60% of 30, calculated by dividing 18 by 30 and then multiplying the result by 100.

Explanation:

Calculating the Percentage

To determine what percentage 18 is of 30, you can use the formula for calculating percentages:

Divide the number you want to find the percentage of (18 in this case) by the total number or 'whole' value (which is 30).

Multiply the result from step 1 by 100 to find the percentage.

So, the calculation is (18 ÷ 30) × 100, which equals 60%. Therefore, 18 is 60% of 30.

There were 980 student desks originally.

Step-by-step explanation:

Number of desks purchased = 295

Desks bought for teacher = 50

Desks for students = No. of desks purchased - desks bought for teachers

Desks for students = 295 - 50 = 245

This is 1/4 of number of original student desks.

Let x be the number of original student desks.

According to statement;

[tex]\frac{1}{4}\ of\ x=245\\\frac{1}{4}x=245[/tex]

Multiplying both sides by 4;

[tex]4*\frac{1}{4}x=245*4\\x=980[/tex]

There were 980 student desks originally.

Keywords: subtraction, multiplication

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Answer:

The relationship between number of animals owned and the number of vet bills is an example positive correlation.

Step-by-step explanation:

Correlation:

Now, as the number of animals increase the number of vet bills will increase. Thus, it could be said that increase in one variable leads to increase in another variable.

Thus, the given relationship is an example of positive relationship or a positive correlation.

Answer:

199.8°

Step-by-step explanation:

The circle has radius r = 7 ft.

Now, the circumference of the circle is given by the formula C = 2πr

So, [tex]C = 2 \times \frac{22}{7} \times 7 = 44[/tex] ft.

Now, 44 ft arc length is equivalent to 360°  

Hence, 24.42 ft arc length is equivalent to [tex]\frac{360}{44} \times 24.42 = 199.8[/tex] degree.

Therefore, the central angle is 199.8° (Answer)