Harold bought 5 apples for $ 1.30. What is the unit price?

marusya05 [52]

Step-by-step explanation:

First solve for y

given equation is 3x-2y ≥ 12

subtract 3x on both sides of the equation which would result with: -2y ≥ 12-3x

divide by -2 on both sides of the equation, flip the sign to ≤ because you are dividing by a negative, then you should get the result y ≤ -6 + 3x/2 (should look like a fraction)

y-intercept is at -6

slope is 3/2 (or three halves)

start at -6 on the y-axis, go up 3 across 2 and plot your point, keep repeating when going up and down the graph

4 0

3 years ago

Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3

exis [7]

Answer:

512

Step-by-step explanation:

when q = 2, w = 3

4q(q + 3w)^2

= 4(2) ((2)+3(3))^2

= 512

6 0

3 years ago

preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha

VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

$X=40$ number of the selected labourers opt for a new incentive scheme.

$n=100$ random sample taken

$\hat p=\frac{40}{100}=0.4$ estimated proportion of the selected labourers opt for a new incentive scheme.

$p$ true population proportion of the selected labourers opt for a new incentive scheme.

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

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

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval 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:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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

And replacing into equation (b) the values from part a we got:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

And rounded up we have that n=369

8 0

3 years ago

If DX/DT= 2cm/s x=-1 y=x^2+1 DY/DT=??

kobusy [5.1K]

Answer:

$\frac{dy}{dt}$ = - 4 cm/s

Step-by-step explanation:

Let us revise the chain rule

If $\frac{dy}{dt}$ = a and $\frac{dx}{dt}$ = b, then

$\frac{dy}{dx}$ = $\frac{dy}{dt}$ ÷ $\frac{dx}{dt}$ = $\frac{a}{b}$

∵ y = x² + 1

- Use the differentiation to find $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2x

∵ x = -1

- Substitute x by -1 in $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2(-1)

∴ $\frac{dy}{dx}$ = -2

∵ $\frac{dy}{dt}$ = $\frac{dy}{dx}$ × $\frac{dx}{dt}$

∵ $\frac{dx}{dt}$ = 2 cm/s

∴ $\frac{dy}{dt}$ = (-2) × (2)

∴ $\frac{dy}{dt}$ = - 4 cm/s

8 0

3 years ago

How can we define appropriate quantities for the purpose of descriptive modeling?

anastassius [24]

Answer:

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays

Step-by-step explanation:

You've assigned your math class a set of word problems. One of the questions ends with, "How many people voted for candidate Jones?" Fingers fly over calculators as your students try to determine the correct answer. After a minute or two, Tommy raises his hand and announces his answer: 4,602.28

Everything inside of you wants to scream, "Are you out of your mind, Tommy boy? A closer answer would be 4 because at least it would be possible! How on earth could a candidate receive 28 hundredths of a vote?"

Okay, breathe. Poor Tommy has made the kind of error that drives math teachers like you to the brink of insanity. He's given an answer that makes absolutely no sense.

Whatever else math is or isn't, it is always logical. Answers should always make sense. Math frequently relies on general knowledge—concepts that we assume are known by everyone over the age of about seven—along with a healthy dose of common sense (not you, Thomas Paine).

The problem, of course, is that people have a tendency to ignore both common sense and the knowledge that they possess. Particularly when calculators are involved, there's the tendency to run with the answer you're given. That ignores one very basic principle: the calculator answers the question you ask, not the one you intended to ask.

This was just an example of Descriptive Modeling

Thank you for asking this question

please choose me as brainiest Answer to support me

3 0

3 years ago