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3 years ago

An artist mixes paint to make new colors.

Mathematics

1 answer:

Tems11 [23]3 years ago

7 0

Answer:

The artist can make six batches of orange paint and it remains one cup of yellow paint

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of red paint for one batch of orange paint = 1/3 of a cup

Amount of yellow paint for one batch of orange paint= 1/3 of a cup

Amount of red paint available = 2 cups

Amount of yellow paint available = 3 cups

2. How many batches of orange paint can she make?

2 cups of red paint = 6/3 = 6 batches of orange paint

3 cups of yellow paint = 9/3 = 6 batches and it remains one cup of yellow paint

The artist can make six batches of orange paint and it remains one cup of yellow paint

Step-by-step explanation:

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Fen completed a triathlon race whose total distance is DDD kilometers. First, she swam a distance of 0.50.50, point, 5 kilometer

Ivanshal [37]

D = 0.5 + 20x + 0.5v

Initial distance covered d1 = 0.5km

If she rode a bicycle for x hours at an average speed of 20 kilometers per hour, then her distance during thus period is,;

Speed = Distance/Time

Distance d2 = speed × time

d2 = 20x

If she ran for 0.5 hour at an average speed of v kilometers per hour, her distance this time will be;

Distance d3 = 0.5v

If her total distance is D, then;

D = d1+d2+d3

D = 0.5 + 20x + 0.5v

Hence an equation that relates D, x, and v is D = 0.5 + 20x + 0.5v

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2 years ago

The object on the right is made from a square-based pyramid joined to a cuboid.

spayn [35]

Answer:

Density of steel = 80.73 gm/ $cm^3$

Step-by-step explanation:

The figure is made up of cuboid and square pyramid.

Height of cuboid, h = 9 cm

Length of cuboid, l = 6 cm

Width of cuboid, w = 6 cm

Volume of cuboid is given by the formula:

$V_{Cuboid} = l \times w \times h$

$V_{Cuboid} = 6 \times 6 \times 9\\\Rightarrow V_{Cuboid} = 324\ cm^3$

Density of Wood , $D_{Cuboid}$ = 0.68g/ $cm^3$

We know that formula of Density is:

$Density = \dfrac{Weight}{Volume}$

$D_{Cuboid} = \dfrac{W_{Cuboid}}{V_{Cuboid}}\\\Rightarrow W_{Cuboid} = V_{Cuboid} \times D_{Cuboid}$

Putting the values:

$W_{Cuboid} = 324 \times 0.68 = 220.32\ gm$

Total weight = $W_{Cuboid} + W_{Pyramid}$

970 = 220.32 $+ W_{Pyramid}$

$W_{Pyramid}$ = 749.68 gm

Volume of pyramid is given as:

$V_{Pyramid}= \dfrac{1}{3} \times \text{Area of Base} \times \text{Vertical Height}$

Base is a square with side 6 cm

$V_{Pyramid}= \dfrac{1}{3} \times 6 \times 6 \times (17 -9)\\V_{Pyramid}= 96\ cm^3$

Density of Steel/Pyramid:

$D_{Pyramid} = \dfrac{W_{Pyramid}}{V_{Pyramid}}\\\Rightarrow D_{Pyramid} = \dfrac{749.68}{96}\\\Rightarrow D_{Pyramid} = 80.73\ gm/cm^3$

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4 years ago

There are five consecutive odd integers. The sum of the three smallest is 3 more than the sum of the two largest. Find the integ

Cerrena [4.2K]

Answer:

11 13 15 17 19

Step-by-step explanation:

We will solve this word problem using 2k+1 which is one of the general forms of an odd integer.

Let 2k+1 be the first odd integer.

(2k+1) + (2k+3) + (2k +5) = (2k+7) + (2k +9) + 3 (the +3 is to accommodate for the left side being 3 more than the right)

Solve for k

6k + 9 = 4k + 19

6k - 4k + 9 = 4k-4k + 19

2k + 9 = 19

2k + 9 - 9 = 19 - 9

2k = 10

2k/2 = 10/2

k = 5

To get the first digit in the series plug in 5 for k

2k+1

2(5) + 1

10 + 1 = 11

So our series is 11, 13, 15, 17, 19

Let's test it.

11 + 13 +15 = 39

17 + 19 = 36

So we are correct, the first 3 integers are 3 more that the sum of the last 2.

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3 years ago

What is the equation of the line that passes through the point (8,-8) and has a slope of -1

marishachu [46]

Answer:

y= (-1)*x

Step-by-step explanation:

lets assume that the line equation is

y=m*x +b

where m is the slope and b the independent variable that intercept Y axis.

then replacing the value of m:

y=(-1)*x + b

after that we have to look for the value of b. Its obtained replaicing the given point (8,-8):

-8 = (-1)*(8) +b

-8 = -8 + b

0 = b

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y= (-1)*x

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3 years ago

Mean variance standard deviation discussions questions

Simora [160]

The answer will be Mean = 135 Variance = 62 and Standard Deviation = 8

<h3>What is the standard deviation? </h3>

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

Given that :

Proportion (p) = 54%

Sample size (n) = 250

Using Normal approximation :

Mean = np

Mean = 250 * 0.54 = 135

Variance = npq ; q = 1 - p = 1 - 0.54 = 0.46

Variance = (250 * 0.54 * 0.46) = 62.1 = 62

Standard deviation = √variance = √62.1

Standard deviation = 7.8803553 = 8

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2 years ago