Which equation has a maximum at y=5 for 0 is less than or equal to x which is less than or equal to 2pi

Rowena can paint a room in $14$ hours, while Ruby can paint it in $6$ hours. If Rowena paints for $x$ hours and Ruby paints for

miv72 [106K]

Question

Rowena can paint a room in 14 hours, while Ruby can paint it in 6 hours. If Rowena paints for x hours and Ruby paints for y hours, they will finish half of the painting, while if Rowena paints for y hours and Ruby paints for x hours they will paint the whole room. Find the ordered pair (x,y)

Answer:

(x, y) = (231/40, 21/40)

where x = 231/40

y = 21/40

Step-by-step explanation:

From the question, we are told:

Rowena can paint a room in = 14 hours

Ruby can paint it in = 6 hours.

This means

In one hour.

Rowena can paint = 1/14 of the room

Ruby can paint =1/6 hour of the room

From the question, we are told that :

If Rowena paints for x hours and Ruby paints for y hours, they will finish half of the painting

This is represented mathematically as:

(1/14)(x) + ( 1/6)(y) = 1/2...... Equation 1

Also we were told that:

if Rowena paints for y hours and Ruby paints for x hours they will paint the whole room

(1/14)(y) + (1/6)(x) = 1 .......... Equation 2

Bringing the two equations together, we have:

(1/14)(x) + ( 1/6)(y) = 1/2 ....... Equation 1

(1/14)(y) + (1/6)(x) = 1 ............ Equation 2

We find the Lowest common multiple of the numerator 14 and 6 = 42. Hence, we multiply both equations through by 42

3x + 7y = 21 ....... Equation 3

7x + 3y = 42 ......... Equation 4

To solve for x and y in Equation 3 and 4 we would be using the Elimination method

21x + 49y = 147 .......... Equation 5

21x +9y = 126 ........... Equation 6

21x + 49y = 147 .......... Equation 5

-(21x +9y = 126) ........... Equation 6

40y = 21

y = 21/40

To get the value of x , we would substitute 21/40 for y in Equation 3

3x + 7y = 21 ....... Equation 3

3x + 7(21/40) = 21

3x + 147/40 = 21

3x = 21 - 147/40

3x = 693/40

x = (693/40) ÷ 3

x = 693/40 × 1/3

x = 693/120

x = 231/40

Therefore, (x, y) = (231/40, 21/40)

7 0

3 years ago

Solve 4x^2 + 43 = 120. Round to the nearest hundredth.

Lady bird [3.3K]

4x² + 43 = 120
4x² = 120 - 43
4x² = 77
x² = 77/4
x² = 19.25
x = ±√19.25
x = ±4.39
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The solutions are ±4.39</span>

4 0

2 years ago

The cost of dell personal computer is $40less than the cost of a gateway computer, while and epson computer cost $70 more than a

kogti [31]

Answer:

Hiii I am srry I dont know the answer but have a nice day!!

Step-by-step explanation:

6 0

2 years ago

An economist wondered if people who go grocery shopping on weekdays go more or less often on Fridays than any other day. She fig

Kamila [148]

Answer:

There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the population proportion.

Proportion in the null hypothesis (p0) = 0.2

Sample size (n) = 75

Sample proportion (sp) = 24/75 = 0.32

Significance level = 0.01

H0: p = 0.2

Ha: p $\neq$ 0.2

Test statistic = (sp - p0) / sqrt ((p0) (1-p0) / n)

Left critical Z value (for 0.01) = -2.5758

Right critical Z value (for 0.01) = 2.5758

Calculated statistic = (0.32 - 0.2) / sqrt ((0.32) (1-0.32) / 75) = 2.2278

Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.

5 0

2 years ago

Does the expression 2b+5b have like terms

ioda

Answer:

7b

the step by step problem

put the two variables together and you get seven b

I know your answer 70

4 0

3 years ago