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2 years ago

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chris and Jana bith measured the distance they live from yhe school. Jana lives closet yhan chris.if chris lives 2/3 mile from t

he school how far does jana live

1 answer:

bixtya [17]2 years ago

3 0

Let x= the distance that Jana lives from school. Then, x < 2/3

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Which system of equations is inconsistent?

Agata [3.3K]

Answer:

Option A is correct.

The system of equation is inconsistent is;

2x+8y=6

5x+20y=2

Explanation:

* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.

* If a system has at least one solution, it is said to be consistent .

*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

(A)

2x+8y=6

5x+20y=2

This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.

(B)

5x+4y=-14

3x+6y=6

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.

(C)

x+2y=3

4x+6y=5

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.

(D)

3x-2y=2

6x-4y=4

this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.

Therefore, the only Option A system of equation is inconsistent.

8 0

2 years ago

Read 2 more answers

Without using a calculator, what is 30% of 546? (You can round up to avoid decimal points)

madreJ [45]

Answer:

Hey there!

We can solve this by multiplying 0.3 by 546, which is about 164.

Hope this helps :)

5 0

2 years ago

Read 2 more answers

The average starting salary for graduates at a university is $25,000 with a standard deviation of $4,000. if a histogram of the

kirill115 [55]

The empirical rule says 68% of the distribution should fall within one standard deviation of the mean, so you should expect salaries between $\$25000-\$4000=\$21000$ and $\$25000+\$4000=\$29000$

3 0

2 years ago

A factory produces weighted balls to use for exercise, by filling spherical rubber shells of different sizes with a sand-like ma

kipiarov [429]

Answer: The radius of the ball must be 5.4 cm

Step-by-step explanation:

The information we have is:

Density of the material = 1.5 g/cm^3

Shell mass = 10 g

we want to find the radius of the ball, such when it is full, the mass is 1 kg.

The mass of the sphere is equal to the density of the material times the volume of the sphere.

The volume of the sphere is:

V = (4/3)*pi*r^3

where pi = 3.14 and r is the radius.

The mass of a filled ball is the mass of the filling material plus the mass of the shell, we have:

mass of the full ball = 1kg = 1000g = (1.5g/cm^3)*((4/3)*pi*r^3) + 10g

1000g = (6.28g/cm^3)*r^3 + 10g

so we must find the value of r.

1000g - 10g = (6.28g/cm^3)*r^3

990g/(6.28g/cm^3) = r^3

157.64cm^3 = r^3

$r = \sqrt[3]{157.64cm^3} = 5.4 cm$

4 0

2 years ago

A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well

kogti [31]

Answer:

Step-by-step explanation:

Hello!

To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:

<u>Group 1</u>: Ate healthy breakfast

X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.

n₁= 26

<u>Group 2: </u>Did not eat healthy breakfast

X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.

n₂= 20

After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:

p'₁= 0.50

p'₂= 0.40

The parameters of study are the population proportions, if the claim is true then p₁ > p₂

And you can determine the hypotheses as

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.05

$Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }$ ≈N(0;1)

pooled sample proportion: $p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46$

$Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67$

p-value: 0.2514

The decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.

At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.

So having a healthy breakfast doesn't seem to improve the grades of students.

I hope this helps!

5 0

2 years ago