What is the equation of the line in slope-intercept form?

Find the next number in the sequence 10,37,82,145,226

ValentinkaMS [17]

$\begin{array}{l|lll} 10&&\\ &+27\to &3^2\cdot 3\\ 37&&\\ &+45\to &3^2\cdot 5\\ 82&&\\ &+63\to &3^2\cdot 7\\ 145&&\\ &+81\to &3^2\cdot 9\\ 226&&\\ &+99\to &3^2\cdot 11\\ \boxed{325}&& \end{array}$

3 0

2 years ago

If the points at (-4, 3) and (2, 3) are reflected over the x-axis to create two new points, what shape can be formed by the four

Svetllana [295]

Answer:

Step-by-step explanation:

Let $(a,b)\in \mathbb{R}^{2}$ , a reflection over the x-axis consists in the following operation:

$(a,b) \rightarrow (a,-b)$

If we know that $X = (-4,3)$ and $Y = (2, 3)$ , then the points translated over the x-axis are $X' = (-4, -3)$ and $Y' = (2,-3)$ , respectively. The most precise description of the shape is a rectangle for the following facts:

1) $XX' = YY' = 8$ and $XY = X'Y' = 6$ .

2) $X$ and $X'$ have the same x-component.

3) $Y$ and $Y'$ have the same x-component.

4) $X$ and $Y$ have the same y-component.

5) $X'$ and $Y'$ have the same y-component.

A representation of the shape is included below as attachment.

3 0

3 years ago

Plleeaassee help it is URGENT MAATHH HELP PLEASE WILL GIVE 5 STARS ON ALL CORRECT ANSWERS, MARK AS BEST ANSWER AND SAY THANKS

lara [203]

Using Pythagoras in the first question
c= $\sqrt{16 ^{2} + 4^{2} } =16.4924$
which is approximately 16.5
for the second question
we also use Pythagoras
$b^2=c^2-a^2$
$\sqrt{13^{2}-12^2}=5$

4 0

3 years ago

Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small com

Rasek [7]

Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.9842

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.

The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6$

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

7 0

3 years ago

What is the shaded area of this figure? Please explain

Ede4ka [16]

I actually don't know how to explain to you, because there's no pointe name.
I just can tell you is use the big square minus the triangle on the top and minus the triangle on the bot.

8 0

3 years ago