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3 years ago

A rectangle has a length of 7 and a width of w. What is an expression for the perimeter?

Mathematics

1 answer:

Nastasia [14]3 years ago

5 0

(7x2)+(2x w). Times 2 because you need each side and the opposite sides are the same size.

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Evaluate this integral. I'm not sure how to evaluate integrals with absolute values.

SOVA2 [1]

Answer:

Step-by-step explanation:

The first step is to understand what the integrand looks like. (See the graph below.)

It is -1 for x < 0 and +1 for x > 0. Thus, the value of this integral is ...

$\int\limits^0_{-1} {-1} \, dx + \int\limits^2_0 {1} \, dx=-1+2=1$

_____

Essentially, you treat the absolute value as a piecewise linear function. This is the same way you treat an absolute value in any equation or inequality.

Here, this means you divide the integral into two parts: one where the integrand is -x/x, and one where it is +x/x.

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3 years ago

The local public transport authority is conducting research into commuter behaviour. A previous census indicated that the mean c

kondor19780726 [428]

Answer:

$H_0:\mu = 45$ and $H_a:\mu < 45$

$T = 34.88$

The null hypothesis is not rejected

Step-by-step explanation:

Given

Random sample of 50 commuter times

Solving (a): The null and alternate hypothesis

From the question, a previous census shows that:

$\mu =45$ and $\sigma= 9.1$

This is the null hypothesis i.e.

$H_0:\mu = 45$

Reading further, a new test was to show whether the average has decreased.

This is the alternate hypothesis, and it is represented as:

$H_a:\mu < 45$

Solving (b) and (c): The test statistic (T).

This is calculated using:

$T = \frac{\mu}{\sigma/\sqrt n}$

In this case:

$n = 50$ $\mu =45$ and $\sigma= 9.1$

So:

$T = \frac{45}{9.1/\sqrt{50}}$

$T = \frac{45}{9.1/7.07}$

$T = \frac{45}{1.29}$

$T = 34.88$

Solving (c): Accept or reject null hypothesis

$\alpha = 0.05$

First calculate the degrees of freedom (df)

$df = n - 1 = 50 - 1$

$d f = 49$

From the t distribution table,

At: $d f = 49$ , $\alpha = 0.05$ and $T = 34.88$

the t score is:

$p = 1.676$

$p > 0.05$

<em>So, the null hypothesis is not rejected</em>

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3 years ago

Can you answer questions 71, and 72?

antiseptic1488 [7]

I think 71 is B
and 72 is D.

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3 years ago

At Lauren's school library, students are allowed to have a balance of no less than -$12 and still check out books. Five days ago

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Yes because the fee will be $2×5(Days)=10 so she can still check out books but she can't have anymore late

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How many hours and minutes are in 700 minutes

Nadusha1986 [10]

I hope this helped you question.... please mark as brainliest

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3 years ago