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3 years ago

Consider the series 1/4+1/6+1/9+2/27+4/81+....

Mathematics

1 answer:

kirza4 [7]3 years ago

5 0

Answer:

The series converges as any two consecutive elements of the sum are monotonically decreasing.

Step-by-step explanation:

The series converges since the consecutive element is monotonically decreasing. That is:

$\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}$ (1)

Where:

$a_{i}$ - The i-th component of the sum.

$a_{i+1}$ - The (i+1)-th component of the sum.

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One afternoon in January, the temperature outside was -4*F. By midnight, the temperature had dropped by 10*F. what was the tempe

loris [4]

The temperature at midnight would be -14*F. Subtract 10 from -4 and you get -14*F

3 0

3 years ago

A professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their class

KIM [24]

Answer:

We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.

Step-by-step explanation:

We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.

He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.

Let p = percentage of seniors who skip their classes.

So, Null Hypothesis, $H_0$ : p $\leq$ 2% {means that seniors skip less than or equal to 2% of their classes}

Alternate Hypothesis, $H_A$ : p > 2% {means that seniors skip more than 2% of their classes}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of seniors who skipped their classes = $\frac{77}{2521}$

n = sample of classes = 2521

So, test statistics = $\frac{\frac{77}{2521} -0.02}{{\sqrt{\frac{\frac{77}{2521}(1-\frac{77}{2521})}{2521} } } } }$

= 3.08

The value of the test statistics is 3.08.

Now at 0.01 significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical value of z as 2.3263 < 3.08, 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 seniors skip more than 2% of their classes.

6 0

4 years ago

the cost of cookies at store A are shown in the graph. The cost y for x cookies at store B is represented by the equation y=o.30

drek231 [11]

Answer:

Step-by-step explanation: pick I because The cookies at store B cost more

5 0

2 years ago

Show that there is no rational number whose square is 5

lozanna [386]

Answer:

Step-by-step explanation:

Take the square root of 5, which is 2.236, aka not a rational number. It doesn't come out to a whole number so therefore there is no rational solution

4 0

3 years ago

Find the ordered pair that makes both the equations below true

NNADVOKAT [17]

Answer:

(3, 1)

Step-by-step explanation:

(a) Algebraic solution

(1) y = -⅔x + 3

(2) y = 2x - 5

Set Equation (1) equal to Equation (2)

-⅔x + 3 = 2x - 5

Multiply each side by 3

-2x + 9 = 6x - 15

Add 15 to each side

-2x + 24 = 6x

Add 2x to each side

24 = 8x

Divide each side by 3

(3) x = 3

Substitute (3) into (2)

y = 2×3 - 5 = 6 - 5 = 1

The ordered pair that makes both equations true is (3, 1).

(b) Graphical solution

In the diagram below, the red line is the graph of Equation (1). The blue line is the graph of Equation (2). The point of intersection is at (3, 1).

7 0

4 years ago