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11111nata11111 [884]
3 years ago
11

Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.

Mathematics
1 answer:
dusya [7]3 years ago
8 0

Answer:

peanuts are more expensive by $1.00.

Step-by-step explanation:

∵ The cost of eight pounds of peanuts = $24.00

∴ The cost of one pound of peanuts = \frac{24}{8}

                                                           = $3.00 per pound

∵ The cost of six pounds of walnuts half as much = \frac{1}{2} \times 24

                                                                               = $12.00

∴ the cost of one pound of walnuts = \frac{12}{6}

                                                           = $2.00 per pound

Difference in the cost per pound = $3.00 - $2.00 = $1.00

Therefore, peanuts are more expensive by $1.00.

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Please can someone help!
Rom4ik [11]

Answer:

51 mph

Step-by-step explanation:

→ The first thing we need is a formula which links speed, distance and time so,

Speed = Distance ÷ Time

Speed = mph

Distance = metres/miles

Time = hours

→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that <em>the car travels at an average speed of 45 mph for 40 minutes, </em>we can rearrange the formula to work out the distance so,

Speed = Distance ÷ Time

→ Rearrange to get distance as subject

Distance = Speed × Time

→ Substitute in the values

Distance = 45 × 40

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

40 ÷ 60 = 0.666666667

→ Substitute in the time value multiplied by the speed

Distance = 45 × 0.666666667 = 30

⇒ 30 metres/miles is overall distance for the first part of the journey

→ Now we have to work out the distance for the second part of the journey. State the distance formula.

Distance = Speed × Time

→ Substitute in the values into the distance formula

Distance = 60 × 25

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

25 ÷ 60 = 0.416666667

→ Substitute in the time value multiplied by the speed

Distance = 60 × 0.416666667 = 25

⇒ 25 metres/miles is overall distance for the second part of the journey

→ Now we have to add the distance of both the journeys together

25 + 30 = 55

→ Then we add the times of the journey together

40 minutes + 25 minutes = 65 minutes

→ Convert 65 minutes into hours

65 ÷ 60 = 1.08333 hours

→ Substitute both values into the speed = distance ÷ time formula

Speed = 55 ÷ 1.08333 = 50.76923077

→ The question says to round it to the nearest whole number so,

50.76923077 = 51 mph

7 0
3 years ago
Simplify. Evaluate the numerical bases. 3^2 b^2 c^-4 *3^-1 b^-5 c^7
photoshop1234 [79]
Hope I can be of assistance!

3^2b^2c^{-4}\cdot \:3^{-1}b^{-5}c^7 \ \textgreater \  \mathrm{Apply\:exponent\:rule}:\ \:a^b\cdot \:a^c=a^{b+c}
3^{-1}\cdot \:3^2=\:3^{2-1}=\:3^1=\:3 \ \textgreater \  3b^{-5}b^2c^{-4}c^7

\mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c} \ \textgreater \  b^{-5}b^2=\:b^{2-5}=\:b^{-3}
3b^{-3}c^{-4}c^7

\mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c} \ \textgreater \  c^{-4}c^7=\:c^{-4+7}=\:c^3
3b^{-3}c^3

\mathrm{Apply\:exponent\:rule}: \:a^{-b}=\frac{1}{a^b} \ \textgreater \  b^{-3}=\frac{1}{b^3} \ \textgreater \  3\cdot \frac{1}{b^3}c^3

\mathrm{Multiply\:fractions}: \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \  \frac{1\cdot \:3c^3}{b^3}

Finally
\mathrm{Apply\:rule}\:1\cdot \:a=a \ \textgreater \  \frac{3c^3}{b^3}

Hope this helps!
8 0
3 years ago
What two numbers multiply to 44 and add up to 12?
djverab [1.8K]
This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.      x*y = 44 ..........(a)

Add up to 12.      x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44   

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.       

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.   

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0,  a = 1, b = -12, c = 44 

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a


x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)    

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number.  Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2      or     (12 - √-32 )/ 2   

x = (12 + 4i√2 )/ 2              (12 - 4i√2 )/ 2 

x = 12/2 + (4i√2)/2                12/2 - (4i√2)/2

x = 6 + 2i√2            or         6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2,  y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2,  y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2


x = 6 + 2i√2,  y = 6 - 2i√2

x = 6 - 2i√2,  y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2
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