A shop owner had three boxes, containing a total of 1500 plastic cups. The number of plastic cups in Box A to the total number of plastic cups was 3:10. He sold 330 plastic cups from Box B and sold 1/3 of the plastic cups in Box C. The number of plastic cups left in Box B to the number of plastic cups left in Box C was 3:1. How many plastic cups were there in Box B at first?

The required perpendicular segment to DE is EF.

In simple geometry, two geometric objects are perpendicular if the intersection at the place of intersection known as a foot results in right angles. The perpendicular symbol can be used to graphically depict the condition of perpendicularity.

In the given diagram we can see that segment DE and EF.

So, we can say that,

Segment DE is perpendicular to segment EF.

Thus, required perpendicular segment to DE is EF.

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Complete question:

The number of integers between two given integers is 124.

The two given integers are 48 and 172.

We know that, number of integers between two integers = Difference of two integers

Here, number of integers = 172-48

= 124

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The equation [tex]24 + n = 39[/tex] may be used to get n, the quantity of scarves Rebecca purchases.

The concept of an equation in algebra is a logical statement that demonstrates the equality of two mathematical equations. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A formula that describes how contain a copy on either sides of a symbol are connected. It typically has an equal sign and one variable. The variable x is included in the preceding example.

The cost of one scarf is $[tex]5[/tex]

The cost of one purse is $[tex]12[/tex]

Rebecca buys 2 purses, so the cost of the purses is [tex]2*12=24[/tex]

The total cost of the purchase is $[tex]39[/tex]

[tex]Total cost = Cost of scarves + Cost of purses[/tex]

[tex]39 = 5n + 24[/tex]

Now we can solve n,

[tex]39 - 24 = 5n[/tex]

[tex]15 = 5n[/tex]

[tex]n = \frac{15}{5}[/tex]

[tex]n=3[/tex]

Therefore, Rebecca buys [tex]3[/tex] scarves.

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Answer: C

Step-by-step explanation:

For A, look at the slope of the graph: 70/2 = 35

For B, slope calculation: m = y-y / x-x = 315-105 / 9-3 = 35

=> C

The vendor's revenue at a price of R1.80 per rose is R9.72

Let's assume that the vendor sells x roses at a price of p per rose.

According to the given condition, if he sells roses at R1.20 per rose, he can sell 350 roses. Hence, we can write:

350 = x - 3((p - 1.20)/0.20)

Simplifying the above equation, we get:

x = 3(p - 0.60) + 350

Now, if the price is increased to R1.80 per rose, the vendor's revenue will be:

Revenue = number of roses sold * price per rose

= (x - 3((1.80 - 1.20)/0.20)) * 1.80

= (x - 15) * 1.80

Substituting the value of x from the first equation, we get:

Revenue = (3(p - 0.60) + 350 - 15) * 1.80

= (3p - 0.30) * 1.80

Simplifying the above equation, we get:

Revenue = 5.4p - 0.54

Therefore, the vendor's revenue at a price of R1.80 per rose is given by the equation 5.4p - 0.54, where p is the price per rose in rands.

To find the vendor's revenue to the nearest cent, we need to substitute p = 1.80 in the above equation:

Revenue = 5.4(1.80) - 0.54

= R9.72 (approx.)

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Answer:

22 rows

Step-by-step explanation:

Divide 48 by 2.25 and round up

The equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.

Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. It involves using algebraic equations and geometric concepts to analyze shapes and figures in a plane or in higher dimensions.

In this equation, -2/3 is the slope of the line, which tells us how steep the line is and in what direction it's heading. Specifically, a slope of -2/3 means that for every increase of 3 units in the x-direction, the y-value decreases by 2 units. So the line slopes downwards from left to right.

The 6 in the equation is the y-intercept of the line, which tells us where the line intersects the y-axis. Specifically, the y-intercept is the point (0, 6) on the line. This means that when x = 0, y = 6, so the line starts at the point (0, 6) on the y-axis.

Therefore, the equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.

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The cot(cos−1(a))= a/√(1-a^2).

Value of cos(sin−1(1)): Let's assume that θ= sin−1(1). It means that sinθ= 1. The value of θ is π/2, therefore we can say that cos(sin−1(1))=cos(π/2)= 0b) Value of tan(cos−1(-23)): Let's suppose that θ= cos−1(-23). It implies that cosθ= -23/25. As we know that tanθ= sinθ/cosθ, Therefore;tan(cos−1(−23))= sin(θ)cos(θ) = -24/25.2. a) Value of sin(cos−1(3/2)): Let's suppose that θ= cos−1(3/2). It implies that cosθ= 3/2. As we know that sin^2θ= 1- cos^2θ, Therefore;sin(cos−1(3/2))= √(1- (3/2)^2)= √(1/4)= 1/2.b) Value of csc(tan−1(-5/1)): Let's assume that θ= tan−1(-5/1). It implies that tanθ= -5/1. As we know that cscθ= 1/sinθ, Therefore;csc(tan−1(−51​))= 1/sin(θ)= 1/√(1+tan^2θ) = 1/√(1+25)= -1/√26.3. a) Value of sin(tan−1(a^2)): Let's suppose that θ= tan−1(a^2). It implies that tanθ= a^2. As we know that sinθ= tanθ/√(1+tan^2θ), Therefore;sin(tan−1(a2​))= (a^2)/√(1+(a^4)).b) Value of cot(cos−1(a)): Let's suppose that θ= cos−1(a). It implies that cosθ= a. As we know that cotθ= cosθ/sinθ, Therefore;cot(cos−1(a))= a/√(1-a^2).

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We might estimate that 0.8n is the approximate prediction number of times it won't land on the elephant.

We need to know the likelihood that the spinner will land on an elephant as well as the total number of spins in order to anticipate the number of times it won't.

Assume the spinner contains five equal parts, one of which is decorated with an elephant. The likelihood of the spinner touching the elephant is then 1/5, or 0.2.

If we know the total number of spins, we can use the likelihood that the spinner will fall on an elephant to calculate the likelihood that it won't. 1 - 0.2 = 0.8 is the probability that the spinner will miss the elephant.

Hence, if we suppose that the spinner is spun n times, we may estimate that 0.8n is the approximate number of times it won't land on the elephant. The prediction of probability of the spinner landing on the elephant is assumed to be constant for each spin and that each spin is independent of the others.

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The factors of 9 are 1 and 9.. To determine this, one can use the formula to find the factors of a number, which is n = a × b.

A counter example to the conditional statement "If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and its self" would be the number 9. 9 is an odd number that is greater than 1 and less than 10, but it has other factors than 1 and itself. The factors of 9 are 1, 3, and 9. To determine this, one can use the formula to find the factors of a number, which is n = a × b, where n is the number, a is the first factor, and b is the second factor. In this case, n = 9, a = 1, and b = 9. Therefore, the factors of 9 are 1 and 9.

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Answer: The answer is 40

Explanation: The picture

The probability of selecting exactly 4 red balls from an urn with 20 red balls and 30 green balls is given by the formula P(X=4) = (20C4)(30C6) / (50C10) where X is the number of red balls chosen. This simplifies to P(X=4) = 0.2032.

On solving the question we have that Therefore, the center of the circle equation is (3/10, -7/10) and the radius is √(1/5).

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

The given equation is that of a circle in standard form:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where the center of the circle is (h, k) and the radius is r.

To convert the given equation to this form, we need to complete the square for both x and y terms. Let's start with the x terms:

[tex]5x^2 - 3x = 5(x^2 - (3/5)x)\\5(x^2 - (3/5)x + (3/10)^2 - (3/10)^2)\\5((x - 3/10)^2 - 9/100)\\5y^2 + 7y = 5(y^2 + (7/5)y)\\5(y^2 + (7/5)y + (7/10)^2 - (7/10)^2)\\5((y + 7/10)^2 - 49/100)\\5((x - 3/10)^2 - 9/100 + (y + 7/10)^2 - 49/100) - 1 = 0\\5(x - 3/10)^2 + 5(y + 7/10)^2 = 1\\[/tex]

Therefore, the center of the circle is (3/10, -7/10) and the radius is √(1/5).

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For the rectangle, the answers will be a. Perimeter=52 inches, b. Perimeter=770 inches and c. Perimeter will be multiplied by 35 also.

What exactly is a rectangle?

A rectangle is a four-sided flat shape with opposite sides that are parallel and equal in length. It is a type of quadrilateral, a polygon with four sides.

Now,

(a) The perimeter of the drawing is the sum of the lengths of all sides of the rectangular garden plus the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right.

The length of the garden in the drawing is 7 inches, and the width is 4 inches. Thus, the perimeter of the garden in the drawing is:

P = 2(7 inches) + 2(4 inches) = 14 inches + 8 inches = 22 inches

Since the garden is surrounded by bricks, we need to add the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right. Each brick has a length of 1 inch, so the total length of the bricks is:

2(1 inch + 7 inches + 1 inch) + 2(1 inch + 4 inches + 1 inch) = 2(9 inches) + 2(6 inches) = 18 inches + 12 inches = 30 inches

Therefore, the perimeter of the drawing is:

22 inches + 30 inches = 52 inches

(b) The actual garden is 35 times larger than the drawing, so its length is 35 × 7 inches = 245 inches, and its width is 35 × 4 inches = 140 inches. Thus, the perimeter of the actual garden is:

P = 2(245 inches) + 2(140 inches) = 490 inches + 280 inches = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden is also multiplied by 35. This is because the perimeter is a linear function of the length and width of the garden. Therefore, the effect on the perimeter of the garden is to increase it by a factor of 35.

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The value of x:z = 1:4.

To find the ratio of x to z, we need to have a common term between x, y, and z. Since we have y in both ratios, we can use it as the common term.

From the given ratios:

x:y = 3:4

y:z = 1:3

We can see that the y in the first ratio and the y in the second ratio are the same.

To find the ratio of x to z, we can "connect" the two ratios by canceling out the y:

x:y = 3:4

y:z = 1:3

x:y × y:z = 3:4 × 1:3

x:z = 3:12

Simplifying the above ratio by dividing both terms by 3, we get:

x:z = 1:4

Your speed is 60 miles per hour, when your friends average speed is 50 miles.

A rational function, which is a function that can be represented as the ratio of two polynomials, is a function that may be used in a rational model, which is a mathematical model. Rates of change, growth or decay, and proportions are only a few examples of the many various kinds of real-world events that may be represented using rational models. In order to describe complicated systems or processes, they are frequently employed in disciplines like economics, physics, and engineering. To determine the values of the variables that make the equation true, rational models can be solved using algebraic techniques including factoring, simplification, and cross-multiplication.

Given that, average speed is 10 miles per hour faster than other person.

Then, your speed is = s + 10.

For 180 miles, and 150 miles for friend the equation can be set as:

180/(s+10) = 150/s

We can cross-multiply to simplify:

180s = 150(s+10)

180s = 150s + 1500

30s = 1500

s = 50

Substituting the value in s + 10 = 50 + 10 = 60.

Hence. your speed is 60 miles per hour.

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Answer:

(0,-2)

Step-by-step explanation:

We found that he can only use approximately 7.39 units of fencing for the fourth side. The possible locations for point H are (4.5, 12.39) and (4.5, -2.39).

To determine where Alex could place point H, we need to first calculate the length of the three sides of the fenced area that he has already plotted. We can do this using the distance formula:

Distance [tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From point E to point F:

Distance = [tex]\sqrt{(6-3)^2 + (5-5)^2}[/tex]

               = 3 units

From point F to point G:

distance = [tex]\sqrt{(9-6)^2 + (1-5)^2)}[/tex]

              = [tex]\sqrt{(9 + 16)}[/tex]

              = 5 units

From point G to point E:

Distance = [tex]\sqrt{(3-9)^2 + (5-1)^2}[/tex]

                = [tex]\sqrt{(36 + 16)}[/tex]

                = [tex]\sqrt{(52)[/tex]

                = [tex]2 \sqrt{(13)}[/tex] units

Therefore, the total length of fencing that Alex has already plotted is 3 + 5 + 2√13 = approximately 14.61 units.

To find the possible x-coordinate(s) of point H, we can use the formula for the distance between two points on the coordinate plane:

distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

For point H to be 7.39 units away from the midpoint of side EF (4.5, 5), we have:

[tex]\sqrt{(x - 4.5)^2 + (y - 5)^2}[/tex]

= 7.39

Squaring both sides and simplifying gives:

(x - 4.5)² + (y - 5)²= 7.39²

Since we know that x=4.5, we can substitute this value into the equation and solve for y:

(4.5 - 4.5)²+ (y - 5)² = 7.39²

(y - 5)² = 7.39²

y - 5 = ±7.39

y = 5 ± 7.39

So the possible locations for point H are (4.5, 5+7.39) and (4.5, 5-7.39), which correspond to the points (4.5, 12.39)

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The length of the second lawn that Sid mows is 60 feet. We simply calculated the area of lawn here.

The area of the first lawn is given by:

A1 = 60 x 50 = 3000 square feet

Let L2 be the length of the second lawn. Since the width of the second lawn is the same as the first lawn, the area of the second lawn can be expressed as:

A2 = L2 x 150

Since the area of the second lawn is 3 times as big as the first lawn, we have:

A2 = 3A1

Substituting A1 and simplifying, we get:

L2 x 150 = 3 x 3000

L2 x 150 = 9000

L2 = 60 feet

Therefore, the length of the second lawn is 60 feet.

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To optimise the volume while maintaining the total dimensions at 7 inches, the camera's dimensions should be roughly 3.01 inches besides 3.311 inches besides 0.679 inches.

What 3 dimensions do we have?

The homes we reside in and the items we use on a daily basis all have three dimensions: length, weigth, and breadth.

Let's start by assigning variables to the dimensions. Let x be the height of the camera, then the length must be 1.1 times the height, which gives us a length of 1.1x.

The width is not explicitly given, but we can express it in terms of x and 1.1x. Since the sum of the dimensions is 7 inches, we have:

x + 1.1x + w = 7

where w is the width of the camera. Simplifying this equation, we get:

2.1x + w = 7

w = 7 - 2.1x

Now we can express the volume of the camera in terms of x:

V = x(1.1x)(7 - 2.1x)

Simplifying this expression, we get:

V = 8.235x³ - 15.365x² + 7x

To find the maximum volume, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, and setting it equal to zero:

dV/dx = 24.705x² - 30.73x + 7 = 0

Using the quadratic formula, we can answer this quadratic equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 24.705, b = -30.73, and c = 7. Plugging in these values, we get:

x = 0.735 inches or x = 3.01 inches

Since x represents the height of the camera, we discard the smaller root and take x = 3.01 inches.

Then the length is 1.1 times the height, which gives us a length of 3.311 inches.

The width can be found using the equation w = 7 - 2.1x, which gives us w = 0.679 inches.

Therefore, the dimensions of the camera should be approximately 3.01 inches by 3.311 inches by 0.679 inches to maximize the volume while keeping the sum of the dimensions at 7 inches.

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Charlotte, North Carolina had an approximate population of  531,145 in 2000.

To approximate Charlotte's population in 2000, we can use the formula for exponential growth:

P(t) = [tex]P0 \times e^{(rt)[/tex]

where P(t) is the population at time t, P0 is the initial population, r is the annual rate of growth as a decimal, and e is the mathematical constant e (approximately 2.71828).

Let's let t = 13 be the number of years between 2000 and 2013. We know that P(13) = 775,000, and r = 0.032. We can solve for P0 as follows:

775,000 = [tex]P0 \times e^{(0.03213)[/tex]

P0 = [tex]775,000 / e^{(0.03213)[/tex]

Using a calculator, we can approximate P0 as:

P0 ≈ 531,145

Therefore, an approximation of Charlotte's population in 2000 is  531,145.

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Answer:

One possible expression that meets the given requirements is:

(2x)/(x+1) = (2x/[(x-2)(x-3)]) / ([(x+1)/(x-2)(x-3)])

This expression simplifies to 2x/(x+1) when x is not equal to -1, 0, 2, or 3, as required.

Explanation: We can rewrite 2x/(x+1) as (2x/(x-2)(x-3)) * ((x-2)(x-3)/(x+1)). The first term in this expression is a division of two rational expressions, while the second term is a multiplication of two rational expressions. Then, we can simplify the first term by cancelling the (x-2)(x-3) terms in the numerator and denominator, which gives 2x/[(x-2)(x-3)]. We can also simplify the second term by expanding the denominator, which gives (x-2)(x-3)/(x-2)(x-3)(x+1) = 1/[(x-2)(x-3)] * 1/(x+1). Then, we can combine the two simplified terms to get the expression given above.

Step-by-step explanation:

Answer:

3.87 miles

Step-by-step explanation:

The attached figure gives the relative locations of the courthouse, the library and the pool.

The three locations represent a right triangle with the distance between courthouse - pool as the hypotenuse and the distance between courthouse - library as the vertical leg

By the Pythagorean theorem if c is the hypotenuse and a, b the other two legs

[tex]c^2 = a^2 + b^2[/tex]

a = distance between courthouse and library = 7 miles
c = distance between courthouse  and pool = 8 miles
and we have to find b

So plugging in known values
[tex]8^2 = 7^2 + b^2\\\\b^2 = 8^2 - 7^2\\\\b^2 = 64 - 49\\\\b^2 = 15\\\\b= \sqrt{15} = 3.87298 \approx 3.87 \;miles[/tex]

Answer:

Let's denote the measures of the other two angles by 13x and 16x, where x is a constant.

Since the sum of the angles in a triangle is always 180 degrees, we can write an equation:

35 + 13x + 16x = 180

Simplifying this equation, we get:

29x = 145

x = 5

Therefore, the measures of the other two angles are:

13x = 13(5) = 65 degrees

16x = 16(5) = 80 degrees

So, the measures of the other two angles are 65 degrees and 80 degrees.

Step-by-step explanation:

Answer:

percentage = (part/whole) x 100

where the "part" is the number of swimmers who finished in less than 39 minutes, and the "whole" is the total number of swimmers.

So, if 29 out of 50 swimmers finished in less than 39 minutes:

percentage = (29/50) x 100

percentage = 58

Therefore, 58% of swimmers finished the race in less than 39 minutes.

An equivalent fraction to represent 58% is 29/50.

Step-by-step explanation:

Step-by-step explanation:

Volume of a cylinder = πr²h

[tex]\pi = 3.14[/tex]

[tex]r = \frac{d}{2} [/tex]

[tex]d = 14[/tex]

[tex]r = \frac{14}{2} [/tex]

[tex]r = 7[/tex]

[tex] {r}^{2} = 49[/tex]

[tex]h = 12[/tex]

substitute the formular with the values above

[tex]3.14 \times 7 \times7 \times 12 = 1846.32[/tex]

To one decimal place

[tex] = 1846.3[/tex]

[tex]1846.3[/tex]

Answer:

(-1,0) and (0, 4)

Step-by-step explanation:

The x and y intercept of a function (say the x intercept), is when y = 0 and vice versa.

The x intercept in this function is when y = 0

Thus,

4x-0=-4

4x = -4

x = -1.

So the x- intercept point = (-1, 0)

Similarly,

4(0)-y= -4

(x is equated to 0 to find the y - intercept)

-y = -4

∴ y = 4

y- intercept point = (0, 4)

Hope this helps! :)

we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.

To solve this problem, we need to find the value of t that corresponds to 31.35 thousand European students. We can use the given equation S=0.05(t3-11t+45t+277) and solve it for t. To do this, we can first subtract 277 from both sides to get S-277=0.05(t3-11t+45t). Then, we can divide both sides by 0.05 to get (S-277)/0.05=t3-11t+45t. Finally, we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.

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