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iren2701 [21]
3 years ago
14

Jake's test scores are 86, 70, 72, 100, 96, and 80. What must Jake earn of his last test to earn a mean grade of exactly 85%?

Mathematics
1 answer:
kompoz [17]3 years ago
4 0

Answer:

91

Step-by-step explanation:

Mean is calculated as

mean = \frac{sum}{count}

let x be his test score of his last test , then

\frac{86+70+72+100+96+80+x}{7} = 85 ( multiply both sides by 7 )

504 + x = 595 ( subtract 504 from both sides )

x = 91

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Given that 1 x2 dx 0 = 1 3 , use this fact and the properties of integrals to evaluate 1 (4 − 6x2) dx. 0
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So, the definite integral  \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

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\int\limits^1_0 {x^{2} } \, dx = 13

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\int\limits^1_0 {(4 - 6x^{2} )} \, dx

<h3>Definite integrals </h3>

Definite integrals are integral values that are obtained by integrating a function between two values.

So, Integral \int\limits^1_0 {(4 - 6x^{2} )} \, dx

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx = \int\limits^1_0 {4} \, dx - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - \int\limits^1_0 {6x^{2} } \, dx \\=  4[x]^{1}_{0}    - 6\int\limits^1_0 {x^{2} } \, dx \\= 4[1 - 0]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4[1]    - 6\int\limits^1_0 {x^{2} } \, dx\\= 4    - 6\int\limits^1_0 {x^{2} } \, dx

Since

\int\limits^1_0 {x^{2} } \, dx = 13,

Substituting this into the equation the equation, we have

\int\limits^1_0 {(4 - 6x^{2} )} \, dx = 4 - 6\int\limits^1_0 {x^{2} } \, dx\\= 4 - 6 X 13 \\= 4 - 78\\= -74

So, \int\limits^1_0 {(4 - 6x^{2} )} \, dx= - 74

Learn more about definite integrals here:

brainly.com/question/17074932

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