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uranmaximum [27]

2 years ago

6

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2. Brian spent £39 that day. Brian now had £4 less than Col

in. How much did Colin initially have?

1 answer:

rosijanka [135]2 years ago

6 0

Answer:

Collin initially have $\£14$

Step-by-step explanation:

Let

x------> money that Brian had initially

y------> money that Collin had initially

we know that

$\frac{x}{y}=\frac{7}{2}$

solve for x

$x=\frac{7}{2}y$ -------> equation A

$x-39=y-4$ ------> equation B

substitute equation A in equation B

$\frac{7}{2}y-39=y-4$

$\frac{7}{2}y-y=39-4$

$\frac{5}{2}y=35$

$y=\£14$

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2 years ago

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Mars2501 [29]

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5 0

2 years ago

Read 2 more answers

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the

larisa [96]

Answer:

No, at the 0.05 significance level, the number of units produced on the night shift is not larger.

Step-by-step explanation:

We are given that the mean number of units produced by a sample of 54 day-shift workers was 345. The mean number of units produced by a sample of 60 night-shift workers was 351.

Assume the population standard deviation of the number of units produced on the day shift is 21 and 28 on the night shift.

Let $\mu_1$ = population mean number of units produced on the day shift

$\mu_2$ = population mean number of units produced on the night shift

So, <u>Null Hypothesis</u>, $H_0$ : $\mu_1-\mu_2\geq0$ or $\mu_1\geq\mu_2$ {means that the mean number of units produced on the night shift is same or lesser on the day shift}

<u>Alternate Hypothesis,</u> $H_A$ : $\mu_1-\mu_2$ or $\mu_1$ {means that the mean number of units produced on the night shift is larger}

The test statistics that will be used here is <u>Two-sample z test statistics</u> as we know about population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1}+\frac{\sigma_2^{2} }{n_2} } }$ ~ N(0,1)

where, $\bar X_1$ = sample mean number of units produced by a sample of 54 day-shift workers = 345

$\bar X_2$ = sample mean number of units produced by a sample of 60 night-shift workers = 351

$\sigma_1$ = population standard deviation of the number of units produced on the day shift = 21

$\sigma_2$ = population standard deviation of the number of units produced on the day shift = 28

$n_1$ = sample of day-shift workers = 54

$n_2$ = sample of night-shift workers = 60

So, <em><u>test statistics</u></em> = $\frac{(345-351)-(0)}{\sqrt{\frac{21^{2} }{54}+\frac{28^{2} }{60} } }$

= -1.302

Now at 0.05 significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -1.302 > -1.6449 so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean number of units produced on the night shift is same or lesser than those produced on the day shift.

4 0

2 years ago

Please, I'm confuse!

Ivahew [28]

OK. You asked for it. Here we go.
First, let's gather up the tools we might use ...
some things that we know about triangles:

-- Every triangle: Area = (1/2) x (length of the base) x (the height)

-- Isosceles triangle: It has two sides that are the same length.

-- Right triangle: It has one right angle in it.
The sides that meet at the right angle are called the "legs".
They form a corner there, like this    _|   .
-------------------------------------------
Now we can start using these tools to hack away at the problem.
Farmer Ted has an isosceles right triangle garden.
The problem asks us to figure out how long the legs are.

Before he changes anything, it looks like this   _|   and both of
those sides are the same length. Call it 'x' until we figure out
what it really is.

Notice that one of them is the base of the triangle, and the other one
is the height. So the area of this triangle is

                           (1/2) (x) (x) or (1/2) x² .

-------------------------------

Farmer Ted is never satisfied. Suddenly, one day without warning, he
comes along and makes the garden bigger. He makes one of the legs
7 ft longer, and he makes the other one 5 ft longer.

Now the length of one leg is (x + 7) and the other one is (x + 5) .
They're still the base and height of the triangle, so the area of the
bigger garden is
                           (1/2) (x + 7) (x + 5).

The problem says that this area is 55 square feet more than the original
area, so look out, here comes the <em>equation </em>:

                       new area         =      old area + bigger

                (1/2) (x + 7) (x + 5) =      (1/2) x² + 55

Locked in the mysterious shadowy crevices of this equation is
everything we need in order to figure out the original length of the legs ...
what we called 'x'.

At this point, we can forget about Farmer Ted, forget about the garden,
and just go back to our laboratory with this equation and solve it to find 'x'.

Let's take it slow and easy, one little step at a time:

                             <u>(1/2) (x + 7) (x + 5) = (1/2) x² + 55</u>

Multiply each side by 2 :       (x + 7) (x + 5) =   x² + 110

Expand (FOIL) the left side:     x² + 12x + 35 =   x² + 110

Subtract x² from each side:          12x + 35 =   110

Subtract 35 from each side:          12x   =      75

Divide each side by 12 :                         <em>x = 6.25 feet</em>

==============================================

OK. That's a very nice number. How do we know whether it's correct ?
Let's check it out, and see if it fits the story:

Original area = (1/2 x base x height) = (0.5 x 6.25 x 6.25) = 19.53125 sq ft

One new leg = (6.25 + 7) =   13.25 ft
Other new leg = (6.25 + 5) = 11.25 ft

New area = (1/2 x base x height) = (0.5 x 13.25 x 11.25) = 74.53125 sq ft

How much bigger is the new area ?

   74.53125 - 19.53125 = <em>55 sq ft </em> yay !

When we start with legs that are 6.25-ft and go through the whole story,
the new area is exactly what the problem says it was. So 6.25-ft is the
correct original length of the legs, before Farmer Ted messed with it.

7 0

2 years ago