What percent tip did the customer leave If he spent $24 on $12 meal?

Lily is cutting a piece of yarn into 3 (three) pieces. The 2nd piece is 3 times as long as the 1st piece, while the 3rd piece is

STatiana [176]

Answer:

The length of the first piece = 41 cm

Step-by-step explanation:

Let the length of the first piece = a

Let the length of the second piece = b

Let the length of the third piece = c

we are given the following:

b = 3a . . . . . (1) (The 2nd piece is 3 times as long as the 1st piece)

c = 6 + a . . . . (2) (the 3rd piece is 6 centimeters longer than the 1st piece)

a + b + c = 211 . . . . . (3) ( the yarn has a total length of 211 centimeters)

Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:

a + b + c = 211

a + (3a) + (6 + a) = 211 ( remember that b = 3a; c = 6 + a)

a + 3a + 6 + a = 211

5a + 6 = 211

5a = 211 - 6 = 205

5a = 205

∴ a = 205 ÷ 5 = 41 cm

a = 41 cm

Therefore the length of the first piece (a) = 41 cm

now finding b and c

substituting a into equation 1 and 2

b = 3a

b = 3 × 41 = 123

∴ b = 123 cm

c = 6 + a

c = 6 + 41 = 47

∴ c = 47 cm

6 0

3 years ago

A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

7 0

3 years ago

Pls help! I need help with a and c I did b already!

laila [671]

Answer:

A= y= -2x+7.

B= y= - $\frac{3}{2}$ x+ 6

Step-by-step explanation:

The linear equation is y=mx+b

A= y= -2x+7.

-2 represents he slope and 7 represents the y intercept.

B= y= - $\frac{3}{2}$ x+ 6

- $\frac{3}{2}$ is the slop and 6 is the y intercept.

Hope this helps :)

8 0

3 years ago

Directions: Set up a system of equations based on the information in the word problem and plz show work 1: The local street cart

aksik [14]

Answer:

2.5x+0.75y=933

x+y=747

Step-by-step explanation:

x= number of cheese sandwiches

y= number of soft drinks

first equation: 2.5x+0.75y=933

**this is representing the cost of the drinks and sandwiches

second equation: x+y=747

**because x and y are the NUMBER of soft drinks and sandwiches, they both have to toal up to 747.

8 0

3 years ago

Can anybody helppp meee please

crimeas [40]

Answer:

r^2=(A/pi)

Step-by-step explanation:

if A=pi*r^2 then maybe dividing by pi to get r^2 alone says r^2=(A/pi) or to get rid of the exponent you may square root each side so r=(sqrt(A/pi))

3 0

3 years ago