Johnny drew a scale drawing of an apartment. The scale he used was 8 inches : 3 feet. In the drawing, the broom closet is 16 inches long. What is the length of the actual closet?

The total change in the number of bushels for sale is 64.1 bushels.

Given

A farmer has 160 bushels of apples to sell at her roadside stand. Every day, she sells around a 13 7/10 bushel.

Let us calculate the overall change in the number of bushels she has available for sale after 7 days.

137/10

Now we'll figure out how many bushels she'll sell in seven days.

7 x 137/10

95.9

In 7 days, the farmer will sell 95.9 bushels. To calculate our overall change, subtract this figure from the total number of bushels of apples.

165 - 95.9 = 64.1

Thus, a total of 64.1 bushels have been added to the amount of bushels available for sale.

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Answer: Two concentric circles have radii $1$ and $2$. Two points on the outer circle are chosen independently and uniformly at random. What is the probability that the chord joining the two points intersects the inner circle?

$\textbf{(A)}\ \frac{1}{6}\qquad \textbf{(B)}\ \frac{1}{4}\qquad \textbf{(C)}\ \frac{2-\sqrt{2}}{2}\qquad \textbf{(D)}\ \frac{1}{3}\qquad \textbf{(E)}\ \frac{1}{2}\qquad$

Solution

Let the center of the two circles be $O$. Now pick an arbitrary point $A$ on the boundary of the circle with radius $2$. We want to find the range of possible places for the second point, $A'$, such that $AA'$ passes through the circle of radius $1$. To do this, first draw the tangents from $A$ to the circle of radius $1$. Let the intersection points of the tangents (when extended) with circle of radius $2$ be $B$ and $C$. Let $H$ be the foot of the altitude from $O$ to $\overline{BC}$. Then we have the following diagram.

[asy] scale(200); pair A,O,B,C,H; A = (0,1); O = (0,0); B = (-.866,-.5); C = (.866,-.5); H = (0, -.5); draw(A--C--cycle); draw(A--O--cycle); draw(O--C--cycle); draw(O--H,dashed+linewidth(.7)); draw(A--B--cycle); draw(B--C--cycle); draw(O--B--cycle); dot("$A$",A,N); dot("$O$",O,NW); dot("$B$",B,W); dot("$C$",C,E); dot("$H$",H,S); label("$2$",O--(-.7,-.385),N); label("$1$",O--H,E); draw(circle(O,.5)); draw(circle(O,1)); [/asy]

We want to find $\angle BOC$, as the range of desired points $A'$ is the set of points on minor arc $\overarc{BC}$. This is because $B$ and $C$ are part of the tangents, which "set the boundaries" for $A'$. Since $OH = 1$ and $OB = 2$ as shown in the diagram, $\triangle OHB$ is a $30-60-90$ triangle with $\angle BOH = 60^\circ$. Thus, $\angle BOC = 120^\circ$, and the probability $A'$ lies on the minor arc $\overarc{BC}$ is thus $\dfrac{120}{360} = \boxed{\textbf{(D)}\: \dfrac13}$.

See Also

answer: 59+16=75

75 total in line

The length of a side of the square is 9 centimeters. The length of the diagonal is 12.73 centimeters.

A square is an object that has four sides of equal length. A square has two diagonals that biscect each other at 90°. The diagonals are of equal length. The diagonals of a square divide the square into two right triangles.

Area of a square = length²

Length = √area

√81 = 9cm

Pythagoras theorem can be used to determine the length of the diagonal.

The Pythagoras theorem: a² + b² = c²

Where:

9²  + 9²

= 81 + 81

= √162 = 12.73 cm

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Answer:

  250 km

Step-by-step explanation:

Sarah traveled a total of 740 km, 2 hours more at a speed of 70 km/h than at a speed of 50 km/h. You want to know how far she traveled at 50 km/h.

The relations between time, speed, and distance are ...

  distance = speed × time

  time = distance/speed

If 'd' represents the distance (km) Sarah traveled by bus (at 50 km/h), then the time (hours) required was ...

  time = d/50

The time at 70 km/h is 2 hours more, and the total distance is ...

  total distance = (distance at 50 km/h) + (distance at 70 km/h)

  740 = d + 70(d/50 +2)

Simplifying the equation, we have ...

  740 = 2.4d +140

  600 = 2.4d . . . . . . . . subtract 140

  d = 250 . . . . . . . . . . . divide by 2.4

Sarah traveled 250 km by bus.

Answer: 8

Step-by-step explanation:

Since the expression is raised to the 3rd power, the highest exponent x will have will be 3. So in order to get the coefficient you multiply 2x by itself 3 times, getting (2x)³ = (2 * 2 * 2)(x * x * x) = (8)(x³) = 8x³

[tex]\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (2x-1)^{3}~\hspace{4em} \begin{array}{cccl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(2x)^{3 }(-1)^0\\ 2&+3&(2x)^{2}(-1)^1\\ 3&+3&(2x)^{1}(-1)^2\\ 4&+1&(2x)^{0}(-1)^3 \end{array} \\\\\\ 1(8x^3)+3(-4x^2)+3(2x)+1(-1)\implies \text{\LARGE 8}x^3-12x^2+6x-1[/tex]

Answer: x<1

Step-by-step explanation:

The most appropriate choice for Profit and loss will be given by-

Cost price of the book is $270

What is Profit and loss?

The price at which an article is bought is known as cost price and the price at which the article is sold is known as selling price.

If the selling price of an article is more than the cost price, the difference between the selling price and the cost price gives the profit.

If the selling price of an article is less than the cost price, the difference between the cost price and the selling price gives the loss.

Here,

Selling price of book = $500

Profit = $230

In case of profit, cost price is always less than the selling price

Cost price of the book = Selling price - profit

                                      = $(500 - 230)

                                       = $270

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Answer:

[tex]y=\dfrac{2}{7}x-12[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given:

The y-intercept is the y-value when x = 0.

Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:

[tex]\implies y=\dfrac{2}{7}x-12[/tex]

The transformations that are needed to transform the graph of f(x) to the graph of g(x) include the following:

In Mathematics, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Given the following function:

Function, f(x) = 4^x

Next, we would translate f(x) 1 unit left based on this horizontal translation rule:

f'(x) = f(x + 1)

f'(x) = 4^{x + 1}

Now, we would apply a vertical translation 3 units down based on this horizontal translation rule:

f''(x) = f'(x) - 3

f''(x) = 4^{x + 1} - 3

Therefore, function g(x) = 4^{x + 1} - 3

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The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

As per the given,

Number of people who vote on their favorite fruit = 9

Number of people who vote for kiwi = 1

The fraction of person vote kiwi to vote on their favorite fruit = 1/9

In decimal form 1/9 =  0.1111111.

Hence "The decimal which represents the fraction of the people who vote for kiwi among all 9 people is 1/9 it's 0.1111111".

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Answer:

tengo

Step-by-step explanation:

i am hispanic

Answer:

21 slices of 3/8 inch

Step-by-step explanation:

Daisy would have 21.This is because 3 times 8 divided by 3 is 8.And 5 times 8 divided by 3 is 13 (you have to ignore the remainder) 8 plus 13 is 21

Step-by-step explanation:

a slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is the ratio (y coordinate change / x coordinate change) when moving from on point on the line to another.

"b" we can read off the graph : when x = 0, then y = -5.

so, b = -5.

for the slope let's pick 2 points. your teacher has kindly marked already points with integer coordinates.

so, I pick (3, 1) and (4, 3).

x changes by +1 (from 3 to 4).

y changes by +2 (from 1 to 3).

so, the slope is

+2/+1 = 2/1 = 2

the equation is

y = 2x - 5

Answer: y=2x-5

Step-by-step explanation:

Choose two points on the graph: (0,-5) and (3,1)

The straight line equation is: y=mx+b

1)

             [tex]\displaystyle\\\boxed {The\ slope\ m\ =\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]\displaystyle\\x_1=0\ \ \ \ \ x_2=3 \ \ \ \ y_1=-5\ \ \ \ y_2=1\\\\ Hence,\\\\m=\frac{1-(-5)}{3-0} \\\\m=\frac{1+5}{3} \\\\m=\frac{6}{3} \\\\m=2\\\\Thus,\ y=2x+b\ \ \ \ \ (1)[/tex]

2)

To determine the coefficient b, take any of the two points,

for example, (0,-5), that is, x=0 y=5

Substitute these values into formula (1):

[tex]-5=2*0+b\\-5=0+b\\-5=b\\Thus,\ b=-5[/tex]

The result is y=2x-5

Answer:

x=2a*b

Step-by-step explanation:

(2x-x)/2a=b

x=2a*b

The perimeter of the rectangle is  32 feet.

Perimeter of the rectangle:

The perimeter of a rectangle is stated that the sum of all the sides of a rectangle.

Through the definition, the perimeter of a rectangle,

P = 2 (a + b) units

where

“a” is the length of the rectangle

“b” is the width of the rectangle

Given,

Here we have the diagram of the rectangle and the measurements are given in it.

And we need to find the perimeter of the rectangle.

Through the given diagram, we know that, the values of

length = 12 feet

width = 4 feet

Now, we have to apply the values on the formula in order to solve it,

So, the perimeter is,

P = 2 ( 12 + 4)

When we simplify it then we get,

P = 2 (16)

After the multiplication we get the result as

P = 32 feet.

Therefore, the perimeter of the rectangle is 32 feet.

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Answer:

  $21.45

Step-by-step explanation:

You want to know the amount of a 9.75% commission on $220.

The amount of the commission is the product of the commission rate and the sales amount to which it is applicable. A 9.75% commission on $220 will be ...

  9.75% × $220 = 0.0975 × $220 = $21.45

Nathan would earn a commission of $21.45 on the sale.

__

Additional comment

We know that a 10% commission can be found by moving the decimal point on the sale amount. A 10% commission on $220 will be $22.

The commission rate of 9.75% is 1/4% less than 10%. 1/4% can be found in two steps: find 1%, then find 1/4 of that.

As with 10%, the 1% amount can be found by moving the decimal point. 1% of $220 is $2.20. One-quarter of that will be $2.20/4 = $1.10/2 = $0.55.

This is the amount we must subtract from the 10% value to make it be 9.75%.

The 9.75% commission amount is $22.00 -0.55 = $21.45.

(The point of using a strategy like this is that you can do the math mentally.)

O P=20($1.50)

If they sell 100 boxes of chocolates, they will make $3,000 in profit.

Given that each chocolate bar costs $1.50 and that there are 20 chocolate bars in a box, multiplication is required to get the profit for the entire box. Using this information, we discover that each chocolate box costs $30, multiplied by 100 boxes to equal $3000.

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Answer:

$9.00

Step-by-step explanation:

if 2 pieces of chicken ordered  --> $3.00

6 pieces of chicken ordered --> x

(cross multiplication)

[tex]x= \frac{6*3}{2}[/tex]

so x = 9

then, 6 pieces of chicken ordered is $9.00

Answer:

The height is 7 units the length is 12 units.

Step-by-step explanation:

It's 6 and 6 for the graph one.

Using it's concept, it is found that:

a) The percent error is of 16.67%.

b) To get the same percent error, the amount of error needs to be the same. Because the estimate was 40 people below the attendance, an estimate of 40 people above the actual attendance will give the same percent error. Therefore, the other estimate that gives the same percent error is an amount of 280 people.

The percent error is given by the difference between the actual and the expected amount, divided by the expected amount and multiplied by 100%.

In the context of this problem, the amounts are given as follows:

Hence the percent error is given as follows:

(240 - 200)/240 x 100% = 16.67%.

For item b, we want to have the same absolute difference between the actual amount and the expected amount, that is:

|Actual - Expected| = 40.

Meaning that there are two possible outcomes:

Which gives the answer to item b, completing the sentences.

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The smallest height of the tower is 24 cm.

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 44 + 3x + 4y = 7 is an expression.

We have,

Grace:

Blocks = 8 cm

Kian:

Blocks = 12 cm

Now,

Grace and Kian both have the same height.

This means,

The least common multiples of 8 and 12.

4 x 2 = 8

4 x 3 = 12

So,

4 x 2 x 3 = 24

Thus,

The smallest height of the tower is 24 cm.

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Answer: 1/343

Step-by-step explanation:

Answer:

$40928.57

Step-by-step explanation:

(5·36500 + 2·52000) / (5 + 2) = 40928.57