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3 years ago

Find the slope and the y-intercept of the line.

Mathematics

1 answer:

Fantom [35]3 years ago

3 0

Answer:

Slope 'm' = $\frac{5}{2}$

And y-intercept = 2

Step-by-step explanation:

Slope-intercept form of a line is given by the equation,

y = mx + b --------(1)

Here, m = slope of the line

b = y-intercept

Given equation is,

5x - 2y = -4

2y = 5x + 4

y = $\frac{5}{2}x+2$

By comparing this equation with equation (1),

Slope 'm' = $\frac{5}{2}$

And y-intercept = 2

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An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from so

alexgriva [62]

Solution :

Let $p_1$ and $p_2$ represents the proportions of the seeds which germinate among the seeds planted in the soil containing $3\%$ and $5\%$ mushroom compost by weight respectively.

To test the null hypothesis $H_0: p_1=p_2$ against the alternate hypothesis $H_1:p_1 \neq p_2$ .

Let $\hat p_1, \hat p_2$ denotes the respective sample proportions and the $n_1, n_2$ represents the sample size respectively.

$$\hat p_1 = \frac{74}{155} = 0.477419$

$n_1=155$

$$p_2=\frac{86}{155}=0.554839$

$n_2=155$

The test statistic can be written as :

$$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}$

which under $H_0$ follows the standard normal distribution.

We reject $H_0$ at $0.05$ level of significance, if the P-value or if $|z_{obs}|>Z_{0.025}$

Now, the value of the test statistics = -1.368928

The critical value = $\pm 1.959964$

P-value = $P(|z|> z_{obs})= 2 \times P(z< -1.367928)$

$=2 \times 0.085667$

= 0.171335

Since the p-value > 0.05 and $|z_{obs}| \ngtr z_{critical} = 1.959964$ , so we fail to reject $H_0$ at $0.05$ level of significance.

Hence we conclude that the two population proportion are not significantly different.

Conclusion :

There is not sufficient evidence to conclude that the $\text{proportion}$ of the seeds that $\text{germinate differs}$ with the percent of the $\text{mushroom compost}$ in the soil.

8 0

3 years ago

HELP! ASAP!

Naily [24]

Answer:

Step-by-step explanation:

Scale= length on drawing / actual length

Let the actual length b x

3:10=2/5/x

3/10=2/5x

Cross multiply

15x=20

x=4/3

The actual length is 4/3

3 0

3 years ago

A carousel horse travels on a circular path with a radius of 15 ft. How many feet does the horse travel over an angle of 2π3 rad

snow_lady [41]

Answer:

$arc\,\,length=10\,\pi\,ft\\arc\,\,length=31.41\,ft$

Step-by-step explanation:

Recall that the formula for the length of an arc of circumference is given by the formula:

$arc\,\,length=\theta\,R$

where $\theta$ is the radian form of central angle subtended , and R is the radius of the circumference. What is important is to have the angle given in radians for this formula to be valid.

In our case, the angle ( $\frac{2\pi}{3}$ ) is already in radians, so we can apply the formula directly:

$arc\,\,length=\theta\,R\\arc\,\,length=\frac{2\,\pi}{3} \,(15\,ft)\\arc\,\,length=10\,\pi\,ft\\arc\,\,length=31.41\,ft$

6 0

3 years ago

Need some help with number word problems, tysm if you do :)

lord [1]

Answer:

Read below

Step-by-step explanation:

x is always the smaller number

y is always the larger number

underlined means it's the question

bolded means it's the answer

1.

One number is 6 times as large as another. Their sum is 42. Find the numbers.

The numbers need to fit the criteria:

6x=y
x+y=42

A. 6+36=42 (correct)

B. 7+42=49 (incorrect)

C. 7+35=42 (incorrect because it doesn't follow the 1st rule)

D. 6+42=48 (incorrect)

Only A. 6, 36 fits the criteria.

2.

One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+3=y
4x-4=3y

4+3=7

12-6≠21 (incorrect)

7+3=10

28-3≠30 (incorrect)

13+3=16

52-4=48 (correct)

9+3≠13 (incorrect)

Only C. 13, 16 fits the criteria.

3.

One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.

The numbers need to fit the criteria:

x+4=y
5x+3=4y

13+4=17

65+3=68 (correct)

-23+4= -19

-115+3≠ -76 (incorrect)

17+4=21

85+3≠84 (incorrect)

-11+4+ -7

-35+3≠ -33 (incorrect)

Only A. 13, 17 fits the criteria.

4.

The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.

The numbers need to fit the criteria:

x+y=23
y-3x=3

5+18=23

18-15=3 (correct)

8+15=23

15-24≠3 (incorrect)

-13+36=23

36+39≠3 (incorrect)

-5+28=23

28+15≠3 (incorrect)

Only A. 5, 18 fits the criteria.

5.

The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.

The numbers need to fit the criteria:

x+y=26
y-2x=2

8+18=26

18-16=2 (correct)

9+17=26

17-18≠2 (incorrect)

7+19=26

19-14≠2 (incorrect)

6+20=26

20-12≠2 (incorrect)

Only A. 8, 18 fits the criteria.

4 0

3 years ago

3 1/8 divided by 1/2

astraxan [27]

Answer:

6.25

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers