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3 years ago

8

Cindy can decorate 84 ornaments in 14 hour. How many ornaments, per hour, can Cindy decorate? A. 3 ornaments per hour O B. 16 or

naments per hour O C. 6 ornaments per hour D. 13 ornaments per hour

1 answer:

just olya [345]3 years ago

8 0

Answer:

6 ornaments

Step-by-step explanation:

Cindy can decorate 84 ornaments in 14 hours

Hence the number of ornaments produced in one hour can be calculated as follows

84 ornaments= 14 hours

x= 1 hour

x= 84/14

= 6

Therefore 6 ornaments can be produced in one hour

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Estimate the quotient using compatible numbers.<br><br> 3,512 ÷ 9<br><br> 30<br> 400<br> 300<br> 40

madreJ [45]

Answer:

400. just use simple devision and it'll tell you.

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3 years ago

Can someone help me? Thanks! :D

Over [174]

Answer:

V = 16 pi h

Step-by-step explanation:

If the diameter is 8, the radius is d/2 =4

The volume is given by

V = pi r^2h

V = pi (4^2)h

V = 16 pi h

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3 years ago

Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?

Deffense [45]

Answer: $-\frac{240}{289}$

=========================================================

Explanation:

Use the pythagorean trig identity $\sin^2(\theta)+\cos^2(\theta) = 1$ and plug in the fact that $\cos(\theta) = \frac{8}{17}\\\\$

Isolating sine leads to $\sin(\theta) = -\frac{15}{17}\\\\$ . I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

$\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\$

6 0

2 years ago

Need help on this math problem!!!

Colt1911 [192]

Answer:

$(fof^{-1})(x)=x$

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ $-\frac{8}{6}$ ]

Another function is the inverse of f(x),

$f^{-1}(x)=-\frac{\sqrt{x}+8}{6}$

Now composite function of these functions will be,

$(fof^{-1})(x)=f[f^{-1}(x)]$

= $[-6(\frac{\sqrt{x}+8}{6})-8]^{2}$

= $[-\sqrt{x}+8-8]^2$

= $(-\sqrt{x})^2$

= x

Therefore, $(fof^{-1})(x)=x$

4 0

3 years ago

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard

dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2$

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

$Z = \frac{106.8 - 104}{2}$

$Z = 1.4$

$Z = 1.4$ has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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3 years ago