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The scale for a scale drawing is 8 millimeters: 1 centimeter. Which is larger,the actual object or the scale drawing?explain

amm1812

The scale is a representation of what the drawing is to real life. The drawing will tend to be represented by a fixed figure such as 1 cm. In this case for every cm of drawing it is a representation of 8 millimetres in real life, therefore the drawing is bigger than the object.

4 0

3 years ago

A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.

yanalaym [24]

X-ounces of an oil blend,
y - ounces of glycerin
x + y = 4 ⇒ y = 4 - x
1.5 x + y = 5.50
1.5 x + 4 - x = 5.50
0.5 x = 5.50 - 4
0.5 x = 1.50
x = 3
y = 4 - 3 = 1
There are 3 ounces of an oil blend and 1 ounce of glycerin.

3 0

3 years ago

Solve the problem algebraically. Clearly define all variables, write an appropriate equation, and solve.

hichkok12 [17]

Answer:

Y=8 and X=21

Step-by-step explanation:

The key to solving word (story) problems is to learn how to translate words and phrases into concise, precise math expressions (variables and operations). Make a table and add to it as you do problems:

is means =

more than +

twice 2*x

sum +

of usually means multiply

...

Assign variables. Try to assign variables to the values the problem asks you to find.

In this problem, there are two variables. Let x = one number; y = other numbers

Translate:

"One number is 5 more than twice the other number" means

x = 5 + 2 * y

"sum of the two numbers is 29" means

x + y = 29

Now, the easy math.

Use the value for x from the first equation and substitute that into the second equation:

(5 + 2y) + y = 29

5 + 3y = 29 (collect terms)

3y = 24 (subtract 5 from both sides)

y = 8

Now, put that value of y into either equation to solve for x (Which equation is easier??)

x + 8 = 29

x = 21 (subtract 8 from both sides)

Checking (very important):

Is 21 really 5 more than 2(8)?

21 = 5+16 ?

21 = 21? yes

Is 21 + 8 = 29 ?

29 = 29? yes

p.s., learn the process, don't just get the right answer; there will be lots of problems that are solved the same way!

3 0

1 year ago

SOLVE THIS PROBLEM ASAP PLS

deff fn [24]

Answer:

See attached

Step-by-step explanation:

-> Also see attached

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

7 0

3 years ago

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

3 years ago