All categories

2 years ago

Find the equation of the line shown. y 3 2 2 3 5 2 2 3 4 5

Mathematics

1 answer:

sergeinik [125]2 years ago

6 0

Answer: $y=\frac{1}{2}x+\frac{1}{2}$

Step-by-step explanation:

The line passes through (-1, 0) and (3,2), so the gradient is $\frac{2-0}{3-(-1)}=\frac{1}{2}$ .

This means the equation of the line is of the form $y=\frac{1}{2}x+c$ for some constant c.

Substituting in the coordinates of the point (-1,0),

$0=\frac{1}{2}(-1)+c\\\\0=-\frac{1}{2}+c\\ \\ c=\frac{1}{2}$

Thus, the equation of the line is $y=\frac{1}{2}x+\frac{1}{2}$

You might be interested in

2564.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A

Leokris [45]

Answer:

We conclude that the board's length is equal to 2564.0 millimeters.

Step-by-step explanation:

We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.

Let $\mu$ = population mean length of the board.

So, Null Hypothesis, $H_0$ : $\mu$ = 2564.0 millimeters {means that the board's length is equal to 2564.0 millimeters}

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 2564.0 millimeters {means that the boards are either too long or too short}

The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s }{\sqrt{n}} }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean length of boards = 2559.5 millimeters

s = sample standard deviation = 15.0 millimeters

n = sample of boards = 26

So, the test statistics = $\frac{2559.5-2564.0}{\frac{15.0 }{\sqrt{26}} }$ ~ $t_2_5$

= -1.529

The value of t-test statistics is -1.529.

Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the board's length is equal to 2564.0 millimeters.

4 0

4 years ago

Tom opens a bank account and makes an initial deposit of $500. The banker tells Tom that he is going to receive

Katena32 [7]

Bank balance after 15 years is $950

Step-by-step explanation:

Step 1: Find the simple interest on the principal amount using the formula SI = PRT/100 where Principal (P) = $500, Rate of Interest (R) = 6% and Time(T) = 15 years

⇒ SI = 500 × 6 × 15/100 = $450

Step 2: Find total amount using the formula Amount = P + SI

⇒ Amount = 500 + 450 = $950

7 0

3 years ago

Find the oth term of the geometric sequence 7, 14, 28, ...

yaroslaw [1]

Answer:

The nth term of the geometric sequence 7, 14, 28, ... is:

$a_n=7\cdot \:2^{n-1}$

Step-by-step explanation:

Given the geometric sequence

7, 14, 28, ...

We know that a geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

where a₁ is the first term and r is the common ratio

Computing the ratios of all the adjacent terms

$\frac{14}{7}=2,\:\quad \frac{28}{14}=2$

The ratio of all the adjacent terms is the same and equal to

$r=2$

now substituting r = 2 and a₁ = 7 in the nth term

$a_n=a_1\cdot r^{n-1}$

$a_n=7\cdot \:2^{n-1}$

Therefore, the nth term of the geometric sequence 7, 14, 28, ... is:

$a_n=7\cdot \:2^{n-1}$

6 0

3 years ago

(-7) x (-7)to the 11th power

masha68 [24]

Answer:

(-7)×(-7)=+49

You change the signs and multiple

5 0

3 years ago

Read 2 more answers

What is the surface area of a triangular prism?

Llana [10]

Answer:

The general formula for the total surface area of a right prism is T. S. A. =ph+2B where p represents the perimeter of the base, h the height of the prism and B the area of the base.

Step-by-step explanation:

5 0

4 years ago