0.08 and 0.4 as fractions in simplest form

A business buys invoice forms at a cost of $4.45 a box for the first 20 boxes, $4.00 a box for the next 25 boxes, and $3.75 a bo

Sergio039 [100]

So the first 20 boxes at 4.45 a piece will total 89.
The next 25 at 4 each will be 100.
Add those and you have 189 dollars, which is a spare of 45.
45/3.75 = 12 .
So the answer is 57

3 0

2 years ago

Rui is a professional deep water free diver.

Vladimir [108]

The correct question is
Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=1/2x^2 -10x What is the lowest altitude Rui will reach?

we have that
d(x)=(1/2)x² -10x

we know that
the function is quadratic (a parabola)
so
the lowest altitude (depth) is the vertex

using a graph tool
see the attached figure

the vertex is the point (10,-50)
that means
His altitude (in meters relative to sea level), 10 seconds after diving is 50 meters under the sea level

therefore
the answer is
the lowest altitude is 50 meters under the sea level

5 0

2 years ago

Read 2 more answers

Suppose you have just enough money, in coins, to pay for a gallon of milk priced at $2.40. You have 12 coins, all quarters and d

wel

The answer is
q + d = 12
0.25q + 0.10d = 2.40

q - the number of quarters
d - the number of dimes

You have 12 coins, all quarters and dimes:
q + d = 12

The value of 1 quarter is $0.25.
The value of 1 dime is $0.10.
Therefore, if you want to pay $2.40 you will have q quarters of value $0.25(0.25q) and d dimes of value $0.10d (0.10d).
The second equation is:
0.25q + 0.10d = 2.40

3 0

2 years ago

A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=17-1=16$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical values.