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3 years ago

What is the exact area of a circle with a radius of 19m

Mathematics

2 answers:

nignag [31]3 years ago

8 0

It is just
19²+π=1,133.54

lilavasa [31]3 years ago

8 0

Area = πr²

= 19²π

= 361 π ≈ 1133.54

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Describe the relationship between n and 4 that will make the value of the expression 6 x n/4 greater than 6.

KatRina [158]

Answer:

n is greater than 4

Step-by-step explanation:

We have to find the relation between n and 4 for which $(6\times \frac{n}{4})$ is greater 6.

Converting this verbal expression into algebraic expression,

$(6\times \frac{n}{4})>6$

$(6\times \frac{n}{6\times 4})>\frac{6}{6}$

$\frac{n}{4}>1$

$\frac{n}{4}\times 4>1\times 4$

n > 4

Therefore, relation between n and 4 is "n is greater than 4".

8 0

3 years ago

The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine puts in the boxes is believed t

krek1111 [17]

Answer:

99.99% probability that the mean weight of a 50-box case of crackers is above 16 ounces

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 16.15, \sigma = 0.3, n = 50, s = \frac{0.3}{\sqrt{50}} = 0.0424$

What is the probability that the mean weight of a 50-box case of crackers is above 16 ounces?

This is 1 subtracted by the pvalue of Z when X = 16. So

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{16 - 16.15}{0.0424}$

$Z = -3.54$

$Z = -3.54$ has a pvalue of 0.0001

1 - 0.0001 = 0.9999

99.99% probability that the mean weight of a 50-box case of crackers is above 16 ounces

3 0

3 years ago

Teresa pays $9.56 for 4 pounds of tomatoes. What is the cost of 1 pound of tomatoes?

Harman [31]

Divide $9.56 by 4 to get the answer
9.56/4=2.39
1 pound of tomatoes is $2.39 each

4 0

4 years ago

Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3

Flauer [41]

$\text{We know that the tangent at any point on a circle is perpendicular}\\
\text{to the radius at that point.}\\
\\
\text{so first we find the equation of the line joining (0,0) and (3,4)}\\
\text{and then using the slope, we find the line perperndicular to it at (3,4)}\\
\\
\text{the equation of the line passing through (0,0) and (3,4) is}\\
\\
y-0=\frac{4-0}{3-0}(x-0)$

$\Rightarrow y=\frac{4}{3}x\\
\\
\text{so the slope of radius is }m=\frac{4}{3}.\\
\\
\text{we know that the product of the perpendicular lines is }-1. \\
\\
\text{so the slope of the perpendicular line would be}=-\frac{1}{4/3}=-\frac{3}{4}\\
\\
\text{So the equation of the tangent line has slope }-\frac{3}{4} \text{ and}\\
\text{passing through (3,4). so equation of tangent line is}$

$y-4=-\frac{3}{4}(x-3)\\
\\
\Rightarrow y-4=-\frac{3}{4}x+\frac{9}{4}\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9}{4}+4\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9+16}{4}\\
\\
\text{so the equation of tangent line is:} y=-\frac{3}{4}x+\frac{25}{4}$

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4 years ago

Write the expression as a polynomial (x+1)(x+2)(y–3)

o-na [289]

$\text{Use FOIL method:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(x+1)(x+2)(y-3)=[(x)(x)+(x)(2)+(1)(x)+(1)(2)](y-3)\\\\=(x^2+2x+x+2)(y-3)=(x^2+3x+2)(y-3)\\\\=(x^2)(y)+(x^2)(-3)+(3x)(y)+(3x)(-3)+(2)(y)+(2)(-3)\\\\=\boxed{x^2y-3x^2+3xy-9x+2y-6}$

6 0

3 years ago