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2 years ago

A teacher surveyed all 120 of her students about their lunch and lunch schedule. The teacher asked two questions:

Mathematics

1 answer:

Sav [38]2 years ago

6 0

you buy lunch and your teacher asks you how much you brought from home then you divide, simple.

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Find the sum of the first 20 terms of an arithmetic sequence with an 18th term of 8.1 and a common difference of 0.25.

il63 [147K]

The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Given,

18th term of an arithmetic sequence = 8.1

Common difference = d = 0.25.

<h3>What is an arithmetic sequence?</h3>

The sequence in which the difference between the consecutive term is constant.

The nth term is denoted by:

a_n = a + ( n - 1 ) d

The sum of an arithmetic sequence:

S_n = n/2 [ 2a + ( n - 1 ) d ]

Find the 18th term of the sequence.

18th term = 8.1

d = 0.25

8.1 = a + ( 18 - 1 ) 0.25

8.1 = a + 17 x 0.25

8.1 = a + 4.25

a = 8.1 - 4.25

a = 3.85

Find the sum of 20 terms.

S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]

= 10 [ 7.7 + 19 x 0.25 ]

= 10 [ 7.7 + 4.75 ]

= 10 x 12.45

= 124.5

Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5

Learn more about arithmetic sequence here:

brainly.com/question/25749583

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8 0

7 months ago

A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears

arsen [322]

Answer:

The correct answer is "0.0000039110".

Step-by-step explanation:

The given values are:

$Y_n\rightarrow N(\mu, \sigma^2)$

$\mu = 40n$

$\sigma^2=100n$

$n=20$

then,

The required probability will be:

= $P(Y_{20}>1000)$

= $P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )$

= $P(Z>\frac{1000-800}{44.7214} )$

= $P(Z>\frac{200}{44.7214} )$

= $P(Z>4.47)$

By using the table, we get

= $0.0000039110$

6 0

2 years ago

Write the equation in slope-intercept form of the line that is parallel to the graph of the equation and passes through the give

Ne4ueva [31]

Answer:

y=x^2 + 3x - 3

Hope it helped :)

4 0

2 years ago

Find the volume and area for the objects shown and answer Question

klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of the given solids.

$\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2$

$\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\$

$\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}$

$\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}$

$SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}$