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3 years ago

The amount that Diego earns at his part time job is proportional to the number of hours he works. he earns $10 per hour.

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

8 0

Answer:

y = 10x

Step-by-step explanation:

Number of hours worked = x
Total earning = y
Earning per hour = $10

The proportional relationship formula for this situation is:

y = 10x

We just substituted k with 10 to represent hourly earning.

jasenka [17]3 years ago

8 0

He earns per hour=10

Let hours be x

He earns in 1 h=10x=10(1)=10
He earns in 2h=10(2)=20

Hence the expression is

$\\ \sf\longmapsto y=10x$

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Help I will be marking brainliest!!!

Keith_Richards [23]

<h3>Answer: A. 18*sqrt(3)</h3>

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

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to choice A as the final answer

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

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

4 0

3 years ago

What is the difference between a line graph and a scatter plot? a. A line graph presents continuous and linked data, while a sca

labwork [276]

A line graph is used to show a trend over a period of time. It is plotted as a series of points, which are then joined with straight lines. The ends of the line graph do not have to join to the axes.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables.

The difference between a line graph and a scatter plot is that a line graph presents continuous and linked data, while a scatter plot presents unlinked data.

6 0

3 years ago

Read 2 more answers

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of

diamong [38]

Answer:

The point estimate for the true difference between the population means is 0.13.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Step-by-step explanation:

To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.

This means that:

$\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325$

A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.

This means that:

$\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753$

Difference between the true mean ages for cars owned by students and faculty.

Distribution s - f. So

$\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13$

This is also the point estimate for the true difference between the population means.

$s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912$

90% confidence interval for the difference:

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

$\alpha = \frac{1 - 0.9}{2} = 0.05$

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 $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs = 1.645*0.2912 = 0.48$

The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years

The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

5 0

3 years ago

List two numbers that are between the two given numbers: 2 3/5 and 2 7/10

Arisa [49]

Answer:

There are many choices, but one answer is 2 3.1/5 and 2 3.2/5.

Step-by-step explanation:

These are equivalent to 2 6.2/10 and 2 6.4/10 which is between both.

(pls mark as brainliest!)

3 0

3 years ago

Andrew bought 3 baseball cards for $240. After a few months, he got an offer from his friend Jack to buy the first card for doub

Dominik [7]

First we define variables:
x = first card original value
y = second card original value
z = third card original value
We write the system of equations:
Andrew bought 3 baseball cards for $ 240:
x + y + z = 240
the first card (at its original value) along with the second card (at its original price) and got $ 320:
2x + y = 320
the first card (at its original value) card along with the third card (at its original price) would have only got him $ 280:
2x + z = 280
Solving the system we have:
x = 120
y = 80
z = 40
Answer:
The original prices for each of the 3 baseball cards is:
(120, 80, 40)

8 0

3 years ago