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3 months ago

What is a31 of the arithmetic sequence for which a5=3.2 and a9=12.0?

Mathematics

1 answer:

zzz [12.3K]3 months ago

7 0

The formula for an arithmetic sequence:

$a_n=a_1+(n-1)d$

We are given:

$a_5=3.2,\ a_9=12.0$

Determine d (the common difference)

$a_9-a_5=4d\\\\4d=12.0-3.2\\\\4d=8.8\ \ \ |:4\\\\d=2.2$

Calculate a31:

$a_{31}=a_5+26d\\\\a_{31}=3.2+26\cdot2.2=60.4$

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At a hot air ballon festival, Erica spots a red ballon due east at an angle of elevation of 36 degrees. She turns due west and s

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Answer:

Step-by-step explanation:

Information provided

The eastern balloon makes an elevation angle of $36^{\circ}$ and is positioned at a height of 461 m.

The western balloon creates an elevation angle of $51^{\circ}$ and is positioned at a height of 296 m.

Considering that Erica is 1.6 m tall, the effective height of the Red balloon becomes 459.4 m,

while the effective height of the Blue balloon ends up at 294.4 m.

Utilizing trigonometric principles,

$\tan 36=\frac{459.4}{d_1}$

$\tan 51=\frac{294.4}{d_2}$

$d_1=632.30 m$

$d_2=238.4 m$

Now calculating the distance separating the two Balloons,

$d=d_1+d_2$

$d=870.70 m$

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3 months ago

Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the b

PIT_PIT [12445]

No, the bat won't fit because 30 divided by 17 equals 1.765

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2 months ago

Read 2 more answers

Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Svet_ta [12734]

It's known that

When two lines are parallel, their slopes are identical.

The slope between any two points can be calculated using the following formula:

$m=\frac{y2-y1}{x2-x1}$

We will calculate the slope for each case to find the solution to the problem.

Case A) Point $B(5,2)\ C(7,-5)$

Determine the slope of BC

Insert the values into the formula:

$m=\frac{-5-2}{7-5}$

$m=\frac{-7}{2}$

$m=-3.5$

Thus,

The equation $y=-3.5x-15$ is parallel to the line that goes through the points $B(5,2)\ C(7,-5)$

Therefore,

the result for Part A) is

$B(5,2)\ C(7,-5)$ ------> $y=-3.5x-15$

Case B) Point $D(11,6)\ E(5,9)$

Calculate the slope of DE

Plug the values into the formula:

$m=\frac{9-6}{5-11}$

$m=\frac{3}{-6}$

$m=-0.5$

Thus,

The equation $y=-0.5x-3$ is parallel to the line that goes through the points $D(11,6)\ E(5,9)$

Therefore,

the result for Part B) is

$D(11,6)\ E(5,9)$ ------> $y=-0.5x-3$

Case C) Point $F(-7,12)\ G(3,-8)$

Determine the slope of FG

Insert the values into the formula:

$m=\frac{-8-12}{3+7}$

$m=\frac{-20}{10}$

$m=-2$

Thus,

Any linear equation with slope $m=-2$ will be parallel to the line through the points $F(-7,12)\ G(3,-8)$

Case D) Point $H(4,4)\ I(8,9)$

Calculate the slope of HI

Substitute the values in the formula:

$m=\frac{9-4}{8-4}$

$m=\frac{5}{4}$

$m=1.25$

Thus,

The equation $y=1.25x+4$ is parallel to the line through the points $H(4,4)\ I(8,9)$

Therefore,

the result for Part D) is

$H(4,4)\ I(8,9)$ ------> $y=1.25x+4$

Case E) Point $J(7,2)\ K(-9,8)$

Determine the slope of JK

Insert the values into the formula:

$m=\frac{8-2}{-9-7}$

$m=\frac{6}{-16}$

$m=-0.375$

Thus,

Any linear equation characterized by slope $m=-0.375$ will be parallel to the line that runs through the points $J(7,2)\ K(-9,8)$

Case F) Point $L(5,-7)\ M(4,-12)$

Find the slope of LM

Substitute the values in the formula:

$m=\frac{-12+7}{4-5}$

$m=\frac{-5}{-1}$

$m=5$

Thus,

The equation $y=5x+19$ is parallel to the line connecting the points $L(5,-7)\ M(4,-12)$

Therefore,

the result for Part F) is

$L(5,-7)\ M(4,-12)$ ------> $y=5x+19$

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3 months ago

Read 2 more answers

Machines at a factory produce circular washers with a specified diameter. The quality control manager at the factory periodicall

zzz [12365]

Answer:

A Type I error could occur if the test shows that the proportion is above 90%, while in reality, the actual proportion is 90%.

Step-by-step explanation:

Machines in a factory produce circular washers that meet a specific diameter.

The quality control manager routinely assesses samples of washers to ensure that more than 90% conform to the specified diameter.

Let p represent the proportion of washers that meet the specified diameter

Thus, Null hypothesis: p = 90% $H_0$

Alternative Hypothesis: p > 90% $H_A$

Here, the null hypothesis posits that the proportion is exactly 90%. In contrast, the alternative hypothesis suggests that the proportion exceeds 90%.

Now, a Type I error indicates the probability of rejecting the null hypothesis while it is actually true or, in simple terms, the likelihood of incorrectly rejecting a valid hypothesis.

Thus, based on our question, a Type I error would declare that the test convincingly indicates the proportion is over 90%, while in truth, it remains 90%.

0 0

2 months ago