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3 years ago

How many inflection point(s) do you see ?

Mathematics

2 answers:

dimulka [17.4K]3 years ago

6 0

Answer:

Step-by-step explanation:

There is a point of inflection at each point where the graph crosses the line y=2. There are 7 points of inflection shown.

A point of inflection is where the graph changes from being concave downward to concave upward, or vice versa. For a sine function, that is everywhere the function crosses its midline.

fenix001 [56]3 years ago

5 0

Answer:

7 inflection points

Step-by-step explanation:

The given function $f(x)=sinx+2$ has a midline of y=2 where each point of the function that intersects the line is an inflection point. Inflection points are where the concavity changes, defined by when the second derivative is equal to 0 or undefined.

$f(x)=sin(x)+2$

$f'(x)=cos(x)$

$f''(x)=-sin(x)$

$0=-sin(x)$

$x=\pi n$ for any integer $n$

From $[-10,10]$ , there are 7 inflection points, which are $x=-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi$

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Do political science classes require less writing than history classes? The 55 randomly selected political science classes assig

saul85 [17]

Answer:

We conclude that political science classes require less writing time than history classes at 0.01 level of significance.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.

Let $\mu_1$ = average writing time required by political science classes.

$\mu_2$ = average writing time required by history classes.

So, Null Hypothesis, $H_0$ : $\mu_1\geq\mu_2$ {means that political science classes require more or equal writing time than history classes}

Alternate Hypothesis, $H_A$ : $\mu_1$ {means that political science classes require less writing time than history classes}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n_1_-_n_2_-_2$

where, $\bar X_1$ = sample average pages of essay writing for political science classes = 16.3 pages

$\bar X_2$ = sample average pages of essay writing for history classes = 18.9 pages

$s_1$ = sample standard deviation for political science classes = 4.8 pages

$s_2$ = sample standard deviation for history classes = 5 pages

$n_1$ = sample of political science classes = 55

$n_2$ = sample of history classes = 54

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }$ = 4.90

So, test statistics = $\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }$ ~ $t_1_0_7$

= -2.77

The value of t test statistics is -2.77.

Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that political science classes require less writing time than history classes.

3 0

3 years ago

A+b=3a simplify plz need ur help asap thx

lozanna [386]

Answer:

a= 1/2b

Step-by-step explanation:

a+b=3a

a=3a-b

a-3a= - b

- 2a= - b

a=1/2b

5 0

4 years ago

Beatrice is purchasing yoga mats from an online store. Each mat costs $8.50, and there is a shipping charge of $12.50 for an ord

Lilit [14]

Answer:

A.7

Step-by-step explanation:

80 - 12.50 = 67.50

67.50 ÷ 8.50 = 7 with a remainder

=7 mats

4 0

3 years ago

What are the solutions to x2 – 10x = 39?

oee [108]

Answer: x=−3 or x=13

Step-by-step explanation:

Step 1: Subtract 39 from both sides.

x2−10x−39=39−39

x2−10x−39=0

Step 2: Factor left side of equation.

(x+3)(x−13)=0

Step 3: Set factors equal to 0.

x+3=0 or x−13=0

x=−3 or x=13

7 0

3 years ago

The sum of three consecutive integers is 192. what are the integers

iVinArrow [24]

Answer:

63, 64, 65

Step-by-step explanation:

Consecutive integers have a difference of 1 between them

let the 3 integers be n, n + 1 and n + 2 , then their sum equals 192

n + n + 1 + n + 2 = 192

3n + 3 = 192 ( subtract 3 from both sides )

3n = 189 ( divide both sides by 3 )

n = 63 ⇒ n + 1 = 64 and n + 2 = 65

the 3 integers are 63, 64 and 65

4 0

3 years ago

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