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3 years ago

15

Darla is playing a computer game to help her learn about science. her scores for the first six games were 9, 12, 10, 8, 14, and

15. how many points does she need to earn on the next game so that her average score for all games is 12 points?

2 answers:

SpyIntel [72]3 years ago

8 0

<h2>Answer:</h2>

The number of points she earned in the next game is:

16

<h2>Step-by-step explanation:</h2>

The scores of the six games is given by:

9, 12, 10, 8, 14, and 15.

Now, let the score in the next game be: x

We know that the average of the scores is the sum of all the score to the total number of scores.

Here the sum of all the scores is:

9+12+10+8+14+15+x=68+x

Also, number of scores= 7

Hence, we have:

$\dfrac{68+x}{7}=12\\\\i.e.\\\\68+x=12\times 7\\\\68+x=84\\\\x=84-68\\\\x=16$

Greeley [361]3 years ago

7 0

Darla would have to score 16 on the next game

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3 years ago

In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To

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Answer:

a

$t = 1.9166$

b

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Step-by-step explanation:

From the question we are told that

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The sample size is $n = 20$

The sample mean is $\= x = 78$

The standard deviation $\sigma = 7$

The level of significance is $\alpha = 0.05$

Now the

Null Hypothesis is $H_o : \mu = 75$

Alternative Hypothesis is $\mu \ne 75$

generally the degree of freedom is mathematically represented as

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$df = 20 -1$

$df = 19$

For a significance level of 0.05 and 19 degrees of freedom, the critical value for the t-test is 2.093. This is obtain from the t-distribution table

The test statistic is mathematically evaluated as

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substituting values

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$t = 1.9166$

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3 years ago

1. Quadrilateral ABCD has vertices A(-1, 1), B(2, 3), C(6, 0) and D(3, -2). Determine using coordinate geometry whether or not t

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Answer:

The Conclusion is

Diagonals AC and BD,

a. Bisect each other

b. Not Congruent

c. Not Perpendicular

Step-by-step explanation:

Given:

[]ABCD is Quadrilateral having Vertices as

A(-1, 1),

B(2, 3),

C(6, 0) and

D(3, -2).

So the Diagonal are AC and BD

To Check

The diagonals AC and BD

a. Bisect each other. B. Are congruent. C. Are perpendicular.

Solution:

For a. Bisect each other

We will use Mid Point Formula,

If The mid point of diagonals AC and BD are Same Then

Diagonal, Bisect each other,

For mid point of AC

$Mid\ point(AC)=(\dfrac{x_{1}+x_{2} }{2},\dfrac{y_{1}+y_{2} }{2})$

Substituting the coordinates of A and C we get

$Mid\ point(AC)=(\dfrac{-1+6}{2},\dfrac{1+0}{2})=(\dfrac{5}{2},\dfrac{1}{2})$

Similarly, For mid point of BD

Substituting the coordinates of B and D we get

$Mid\ point(BD)=(\dfrac{2+3}{2},\dfrac{3-2}{2})=(\dfrac{5}{2},\dfrac{1}{2})$

Therefore The Mid point of diagonals AC and BD are Same

Hence Diagonals,

a. Bisect each other

B. Are congruent

For Diagonals to be Congruent We use Distance Formula

For Diagonal AC

$l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting A and C we get

$l(AC) = \sqrt{((6-(-1))^{2}+(0-1)^{2} )}=\sqrt{(49+1)}=\sqrt{50}$

Similarly ,For Diagonal BD

Substituting Band D we get

$l(BD) = \sqrt{((3-2))^{2}+(-2-3)^{2} )}=\sqrt{(1+25)}=\sqrt{26}$

Therefore Diagonals Not Congruent

For C. Are perpendicular.

For Diagonals to be perpendicular we need to have the Product of slopes must be - 1

For Slope we have

$Slope(AC)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Substituting A and C we get

$Slope(AC)=\dfrac{0-1}{6--1}\\\\Slope(AC)=\dfrac{-1}{7}$

Similarly, for BD we have

$Slope(BD)=\dfrac{-2-3}{3-2}\\\\Slope(BD)=\dfrac{-5}{1}$

The Product of slope is not -1

Hence Diagonals are Not Perpendicular.

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4 years ago