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3 years ago

What is the slope of the line represented by the equation 2x+3y= –12 ? –32 –23 23 32

Mathematics

2 answers:

malfutka [58]3 years ago

8 0

Answer:

the answer is -2/3

Step-by-step explanation:

i took the test

mr_godi [17]3 years ago

7 0

Answer:

Option 2 - $m=-\frac{2}{3}$ is the slope of the equation.

Step-by-step explanation:

Given : Equation $2x+3y=-12$

To find : What is the slope of the line represented by the equation ?

Solution :

The slope form of line is $y=mx+c$

Equation $2x+3y=-12$

Take 2x to another side,

$3y=-12-2x$

Divide 3 both side,

$y=\frac{-12-2x}{3}$

$y=\frac{-2}{3}x-4$

On comparing with general equation,

$m=-\frac{2}{3}$ is the slope of the equation.

Therefore, option 2 is correct.

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Step-by-step explanation:

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A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they

zalisa [80]

Answer:

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Step-by-step explanation:

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3 years ago

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Refer to the following scenario:You want to see if there is a difference between the exercise habits of Science majors and Math

bekas [8.4K]

Answer:

1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

$p_1=X_1/n_1=82/135=0.607$

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

$p_2=X_2/n_2=41/92=0.446$

The difference between proportions is (p1-p2)=0.162.

$p_d=p_1-p_2=0.607-0.446=0.162$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$\text{P-value}=2\cdot P(z>2.4014)=0.0171$

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

$MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335$

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

6 0

3 years ago

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perim

olga55 [171]

*The side with the middle length is 12cm, therefore BC must be 12 cm

------------------------------------------------------------
Ratio
-----------------------------------------------------------
BC:AC:AB
4 : 3 : 5

-----------------------------------------------------------
Find 1 share
-----------------------------------------------------------
Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm

-----------------------------------------------------------
Find AC (4 shares)
-----------------------------------------------------------
3 shares = 3 x 3 = 9 cm
BC = 9cm

-----------------------------------------------------------
Find AB (5 shares)
-----------------------------------------------------------
5 shares = 5 x 3 = 15cm
AB = 15cm

------------------------------------------------------------
Length
-----------------------------------------------------------
BC : AC : AB
12cm : 9cm : 15cm

------------------------------------------------------------------
Perimeter
------------------------------------------------------------------
12 + 9 + 15 = 36cm

------------------------------------------------------------------
Answer: The perimeter is 36cm
------------------------------------------------------------------

------------------------------------------------------------------
Area
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1/2 x 9 x 12 = 54cm²

------------------------------------------------------------------
Answer: Area = 54cm²
------------------------------------------------------------------

Given that the biggest ratio is AB
⇒AB is the hypotenuse
AB = 15 cm

------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
------------------------------------------------------------------

8 0

3 years ago

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