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3 years ago

Find the arc length of the

Mathematics

2 answers:

musickatia [10]3 years ago

6 0

Answer:

3.5 $\pi$

Step-by-step explanation:

Khan academy

Agata [3.3K]3 years ago

4 0

Answer:

Circle circumference = radius * 2 * PI

Arc Length = radius * 2 * PI * Central Angle / 360 degrees

Arc Length = 7 * 2 * PI * (1/4)

= 3.5 * PI

= 10.9955742876

Arc Length = 10.996 (rounded)

Step-by-step explanation:

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It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work i

Salsk061 [2.6K]

Answer:

$(-\infty, 0.2661)$

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

n=60 represent the sample size

X=12 represent the number of masks that had lenses pop out at 250°

$\hat p =\frac{12}{60}=0.2$ represent the estimated proportion of masks that had lenses pop out at 250°

p represent the population proportion of masks that had lenses pop out at 250°

Confidence =0.9 or 90%

$\alpha=0.1$ represent the significance level

Confidence interval

On this case we want a interval on this form : $(-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})$

So the critical value would be on this case $z_{\alpha}=1.28$ and we can use the following excel code to find it: "=NORM.INV(1-0.1,0,1)"

We found the lower limit like this:

$0.2 +1.28\sqrt{\frac{0.2 (1-0.2)}{60}}=0.2661$

And the interval would be: $(-\infyt, 0.2661)$

3 0

3 years ago

How do i solve this?<br>13=x/4

Alex17521 [72]

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

13-(x/4)=0

Step by step solution :

Step 1 :

Simplify —

Equation at the end of step 1 :

13 - — = 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 4 as the denominator :

13 13 • 4

13 = —— = ——————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

13 • 4 - (x) 52 - x

———————————— = ——————

4 4

Equation at the end of step 2 :

52 - x

—————— = 0

Step 3 :

When a fraction equals zero :

Now, to get rid of the denominator, Tiger multiple's both sides of the equation by the denominator. 3.1 When a fraction equals zero …

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Here's how:

52-x

———— • 4 = 0 • 4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

52-x = 0

Solving a Single Variable Equation :

3.2 Solve : -x+52 = 0

Subtract 52 from both sides of the equation :

-x = -52

Multiply both sides of the equation by (-1) : x = 52

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2 years ago