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1 year ago

Giselle works as a carpenter and as a

Mathematics

1 answer:

Ad libitum [116K]1 year ago

4 0

Answer:

12 hours as a carpenter and 18 as a blacksmith.

Step-by-step explanation:

So she earns 20$ per hour as a carpenter. c can represent the amount of hours she worked as a carpenter, and the coefficient will be 20 (salary)

So she earns 25$ per hour as a blacksmith, b can represent the amount of hours she worked as a blacksmith, and 25 will be the coefficient (salary)

So we have the two equations:

c + b = 30

20c + 25b = 690

Now we can solve for c in terms of b and substitute that into the second equation:

Original equation:

c + b = 30

Subtract b from both sides

c = -b + 30

Original equation:

20c + 25b = 690

Substitute -b + 30 as c

20(-b + 30) + 25b = 690

Distribute the 20

-20b + 600 + 25b = 690

Simplify the equation

600 + 5b = 690

Subtract 600 from both sides

5b = 90

Divide both sides by 5

b = 18

Now plug this into either of the original equations to solve for c, but the first equation b + c = 30 is the easiest, so I'll use that equation

Original equation

b + c = 30

Substitute 18 as b

18 + c = 30

Subtract 18 from both sides

12 = c

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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2 years ago

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The horizontal line segment at the top of the polygon on the grid below is how many units long?

Ymorist [56]

Answer:

6 units long.

Step-by-step explanation:

Given:

A polygon drawn on a graph.

In order to determine the distance of the horizontal line at the top, we find the coordinates of the end points and then use distance formula to find the exact distance.

Let us label the polygon as ABCD as shown below. AB is the length of the horizontal line.

Coordinates of A are $(x_1,y_1)=(-3, 4)$ as seen in the graph.

Coordinates of B are $(x_2,y_2)=( 3, 4)$ as seen in the graph.

Now, distance formula for two points $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d_{AB}=\sqrt{(3-(-3))^2+(4-4)^2}\\d_{AB}=\sqrt{(3+3)^2+0}\\d_{AB}=\sqrt{36}=6\ units$

Therefore, the horizontal line at the top is 6 units long.

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3 years ago

A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 13.6

dimaraw [331]

Answer:

The confidence interval is $13.4< \mu < 13.8$

Step-by-step explanation:

From the question we are told that

The sample mean is $\= x = 13.6$

The standard deviation is $\sigma = 1.9$

The sample size is $n = 189$

given that the confidence level is 85% then the level of significance is mathematically represented as

$\alpha = (100 - 85 )\%$

$\alpha = 0.15$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{\alpha }{2} } = 1.44$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.44* \frac{1.9}{\sqrt{189} }$

=> $E = 0.1990$

The 85% confidence interval is mathematically represented as

$\= x - E < \mu$

=> $13.6- 0.1990 < \mu < 13.6+ 0.1990$

=> $13.4< \mu < 13.8$

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3 years ago