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Ierofanga [76]
2 years ago
6

The sum of three consecutive even integers is 78. Find the three integers.

Mathematics
1 answer:
qaws [65]2 years ago
3 0

Answer:

24, 26, and 28

Step-by-step explanation:

They are all even and they are consecutive even integers that equal 78 when added up

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Find y’ for y=7sec^3x
laiz [17]
Taking the derivative of 7 times secant of x^3:
We take out 7 as a constant focus on secant (x^3)
To take the derivative, we use the chain rule, taking the derivative of the inside, bringing it out, and then the derivative of the original function. For example:
The derivative of x^3 is 3x^2, and the derivative of secant is tan(x) and sec(x).
Knowing this: secant (x^3) becomes tan(x^3) * sec(x^3) * 3x^2. We transform tan(x^3) into sin(x^3)/cos(x^3) since tan(x) = sin(x)/cos(x). Then secant(x^3) becomes 1/cos(x^3) since the secant is the reciprocal of the cosine.

We then multiply everything together to simplify:

sin(x^3) * 3x^2/ cos(x^3) * cos(x^3) becomes

3x^2 * sin(x^3)/(cos(x^3))^2

and multiplying the constant 7 from the beginning:

7 * 3x^2 = 21x^2, so...

our derivative is 21x^2 * sin(x^3)/(cos(x^3))^2


6 0
3 years ago
Solve the equation 2/3-4x+7/2=-9x+5/6
VMariaS [17]

Answer:

<u>For this equation the value of x is - 2/3</u>

Step-by-step explanation:

1. Resolving the equation 2/3-4x+7/2=-9x+5/6

-4x + 9x = 5/6 - 2/3 - 7/2 (Putting the all the x values on the left)

5x = (5/6 - 4/6 -21/6)

5x = -20/6

x = - 20/6 /5 (Dividing by 5 at both sides)

x = -20/6 * 1/5

<u>x = -4/6 = - 2/3 (Simplifying)</u>

2. Proof of replacing x by -2/3

2/3 - 4 (-2/3) + 7/2 = -9 (-2/3) + 5/6

2/3 + 8/3 + 7/2 = 18/3 + 5/6

10/3 + 7/2 = 6 + 5/6

20 + 21 = 36 + 5 (Multiplying by 6 at both sides)

41 = 41

<u>It means the value of -2/3 for x is correct</u>

Note: Same answer than 13866851

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3 years ago
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a s
Andrew [12]

Answer:

a) 1186

b) Between 1031 and 1493.

c) 160

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean of 1262 and a standard deviation of 118.

This means that \mu = 1262, \sigma = 118

a) Determine the 26th percentile for the number of chocolate chips in a bag. ​

This is X when Z has a p-value of 0.26, so X when Z = -0.643.

Z = \frac{X - \mu}{\sigma}

-0.643 = \frac{X - 1262}{118}

X - 1262 = -0.643*118

X = 1186

(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.

Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a p-value of 0.025, so X when Z = -1.96.

Z = \frac{X - \mu}{\sigma}

-1.96 = \frac{X - 1262}{118}

X - 1262 = -1.96*118

X = 1031

97.5th percentile:

X when Z has a p-value of 0.975, so X when Z = 1.96.

Z = \frac{X - \mu}{\sigma}

1.96 = \frac{X - 1262}{118}

X - 1262 = 1.96*118

X = 1493

Between 1031 and 1493.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Difference between the 75th percentile and the 25th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

Z = \frac{X - \mu}{\sigma}

-0.675 = \frac{X - 1262}{118}

X - 1262 = -0.675*118

X = 1182

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

Z = \frac{X - \mu}{\sigma}

0.675 = \frac{X - 1262}{118}

X - 1262 = 0.675*118

X = 1342

IQR:

1342 - 1182 = 160

7 0
3 years ago
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