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3 years ago

What is the area of this figure? Nearest tenth. Use 3.14 for pi if needed.

Mathematics

1 answer:

stira [4]3 years ago

4 0

Answer:

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Step-by-step explanation:

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3. I opened a compound interest account with $300 at 2%. How much money will be in the

MArishka [77]

Answer:

there will be 408$ at the end of 18 months

Step-by-step explanation:

2% of 300 is 6 and 6 x 18 = 108. 108 + 300 = 408

8 0

3 years ago

Read 2 more answers

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seedlings. Using a hydroponics grow p

Ede4ka [16]

Answer:

1) The mean calculated for this case is $\bar X=61.5$

2) $61.5-5.4=56.1$

3) $61.5+5.4=66.9$

4) B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Part 1

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (a)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (b)

The mean calculated for this case is $\bar X=61.5$

The sample deviation calculated $s=5.143$

$\mu$ population mean (variable of interest)

n=6 represent the sample size

Part 2

The confidence interval for the mean is given by the following formula:

$\bar X \pm ME$ (1)

So if we have the margin of error 5.4mm we can find the lowr limit like this:

$61.5-5.4=56.1$

Part 3

$61.5+5.4=66.9$

Part 4

B. An interval estimate gives us a sense of the accuracy of the point estimate whereas a point estimate alone does not.

Because with the confidence interval we know the confidence level of the interval, and the limits for the parameter at some significance level.

4 0

4 years ago

Read 2 more answers

Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o

Brrunno [24]

Answer:

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

$Sin\ C = \frac{h}{a}$

Make h the subject:

$h = aSin\ C$

Also, in BOC (Using Pythagoras)

$a^2 = h^2 + x^2$

Make $x^2$ the subject

$x^2 = a^2 - h^2$

Substitute $aSin\ C$ for h

$x^2 = a^2 - h^2$ becomes

$x^2 = a^2 - (aSin\ C)^2$

$x^2 = a^2 - a^2Sin^2\ C$

Factorize

$x^2 = a^2 (1 - Sin^2\ C)$

In trigonometry:

$Cos^2C = 1-Sin^2C$

So, we have that:

$x^2 = a^2 Cos^2\ C$

Take square roots of both sides

$x= aCos\ C$

In triangle BOA, applying Pythagoras theorem, we have that:

$AB^2 = h^2 + (b-x)^2$

Open bracket

$AB^2 = h^2 + b^2-2bx+x^2$

Substitute $x= aCos\ C$ and $h = aSin\ C$ in $AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = h^2 + b^2-2bx+x^2$

$AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2$

Open Bracket

$AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C$

Reorder

$AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C$

Factorize:

$AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C$

In trigonometry:

$Sin^2C + Cos^2 = 1$

So, we have that:

$AB^2 = a^2 * 1 + b^2-2abCos\ C$

$AB^2 = a^2 + b^2-2abCos\ C$

Take square roots of both sides

$AB = \sqrt{a^2 + b^2-2abCos\ C}$

6 0

3 years ago

3x2 - 5x + 6) + (9 - 8x - 4x2)

Ksju [112]

Answer:

13-13x

Step-by-step explanation:

3*2=6

(6-5x+6) + (9-8x-8)

Combine Like Terms

(12-5x) + (1-8x)

Put x on one side and numbers on the other.

(12+1) + (-5x+ (-8x))

13-13x

8 0

3 years ago

Please help! Will mark brainiest!!!!

brilliants [131]

Answer:

This is the alternate exterior angle theorem

Step-by-step explanation:

This is because angle 2 and angle 7 are in the <u>outer</u> part of each side of opposite lines

8 0

3 years ago