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strojnjashka [21]

2 years ago

14

At a historical landmark, candles are used to simulate an authentic atmosphere. A volunteer is currently putting new candles in

the candle holders. On the east side, he replaced candles in 24 small candle holders and 3 large candle holders, using a total of 87 candles. On the west side, he replaced the candles in 14 small candle holders and 7 large candle holders, for a total of 77 candles. How many candles does each candle holder hold?
Each small candleholder holds ____ candles, and each large one holds ____ candles

1 answer:

myrzilka [38]2 years ago

5 0

Answer:

Each small candleholder holds 3 candles, and each large one holds 5 candles.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of candles that a small candleholder holds.

y is the number of candles that a large candleholder holds.

24 small candle holders and 3 large candle holders, using a total of 87 candles.

This means that

$24x + 3y = 87$

Simplifying by 3

$8x + y = 29$

$y = 29 - 8x$

14 small candle holders and 7 large candle holders, for a total of 77 candles.

This means that $14x + 7y = 77$

Simplifying by 7

$2x + y = 11$

$y = 11 - 2x$

Since $y = 29 - 8x$

$11 - 2x = 29 - 8x$

$6x = 18$

$x = \frac{18}{6}$

$x = 3$

$y = 29 - 8x = 29 - 8*3 = 29 - 24 = 5$

Each small candleholder holds 3 candles, and each large one holds 5 candles.

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madam [21]

Answer:

(x + 3) ( x - 6)

Step-by-step explanation:

x² - 3x - 18

x² - 6x + 3x - 18

x(x - 6) + 3(x - 6)

(x + 3) ( x - 6)

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3 years ago

Read 2 more answers

A line passes through point (3, 7) and has a slope of 3/4. the equation of the line is . if point a (x,5) lies on the line, the

kvv77 [185]

7 = 3/4 (3) + c
28 = 9 + 4c
4c = - 19
c = - 19/4
y = 3/4x - 19/4

5 = 3/4x - 19/4
3/4x = 39/4
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5 0

2 years ago

mr_godi [17]

Answer:

$V = \frac{2L\sqrt{3}}{3} \pi}$

$A = 4\pi + \sqrt{3L^{2} + 16}$

Step-by-step explanation:

Figure of cone is missing. See attachment

Given

Radius, R = 2m

Let L = KL=LM=KM

Required:

Volume, V and Surface Area, A

<u><em>Calculating Volume</em></u>

Volume is calculated using the following formula

$V = \frac{1}{3} \pi R^{2} H$

Where R is the radius of the cone and H is the height

First, we need to determine the height of the cone

The height is represented by length OL

It is given that KL=LM=KM in triangle KLM

This means that this triangle is an equilateral triangle

where OM = OK = $\frac{1}{2} KL$

OK = $\frac{1}{2}L$

Applying pythagoras theorem in triangle LOM,

|LM|² = |OL|² + |OM|²

By substitution

L² = H² + ( $\frac{1}{2}L$ )²

H² = L² - $\frac{1}{4}L$ ²

H² = L² (1 - $\frac{1}{4}$ )

H² = L² $\frac{3}{4}$

H² = $\frac{3L^{2} }{4}$

Take square root of bot sides

$H = \sqrt{\frac{3L^{2} }{4}}$

$H = \frac{L\sqrt{3}}{2}$

Recall that $V = \frac{1}{3} \pi R^{2} H$

$V = \frac{1}{3} \pi 2^{2} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi * 4} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi} * {2L\sqrt{3}}$

$V = \frac{2L\sqrt{3}}{3} \pi}$

in terms of $\pi$ an d L where L = KL = LM = KM

<u><em>Calculating Surface Area</em></u>

Surface Area is calculated using the following formula

$H = \frac{L\sqrt{3}}{4}$

$A=\pi r(r+\sqrt{h^{2} +r^{2} } )$

$A=\pi * 2(2+\sqrt{((\frac{L\sqrt{3}}{2})^{2} +2^{2} } )$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}}{4} } + 4 }$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A=2\pi(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{\sqrt{4}} )$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{2} )$

$A = 2\pi (2 + {\frac{1}{2} \sqrt{3L^{2} + 16})$

$A = 4\pi + \sqrt{3L^{2} + 16}$

6 0

2 years ago

(Hypothetical.) Suppose five measurements of the volume of a liquid yield the following data (in milliliters).

ElenaW [278]

Answer:

(48.106 ; 53.494)

Step-by-step explanation:

Given the data:

X : 52 48 49 52 53

Sample mean = ΣX / n

n = 5

Sample mean, xbar = 254 / 5 = 50.8

Standard deviation, s = 2.17 (using calculator)

The standard error (SE) : s/√n =2.17/√5 = 0.970

The degree of freedom, df = n-1

df = 5 - 1 = 4

Tscore(0.05, 4) = 2.776

Confidence interval :

Xbar ± Tscore*standard error

50.8 ± (2.776 * 0.970)

50.8 ± 2.694

Lower boundary = 50.8 - 2.694 = 48.106

Upper boundary = 50.8 + 2.694 = 53.494

(48.106 ; 53.494)

7 0

2 years ago

A line passes through the origin and has a slope of 1/2.

ArbitrLikvidat [17]

Answer:

(2, 1)

Step-by-step explanation:

A line that passes through the origin and has a slope of 1/2 can be best represented as y = 1/2x

it starts at the origin

goes 2 units to the right

1 unit above

2 units to the right + 1 unit above = (2, 1)

Final Answer: (2, 1)

8 0

2 years ago