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3 years ago

8

One way to build a staircase is to attach triangular blocks to an angled support, as shown above. If the support makes a 32 angl

e with the floor, what must the measure of angle 1 be so that the steps are parallel to the floor?

1 answer:

Ivan3 years ago

3 0

All the angels ect would have to be equal to all of them dose it tell u the angels

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Evaluate ƒ(x) = 3x + 8 for x = 1.

sesenic [268]

F equals 11 because it three times 1 plus eight.

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3 years ago

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The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

Hoochie [10]

Answer:

Step-by-step explanation:

Hello!

X: number of gypsy moths in a randomly selected trap.

This variable is strongly right-skewed. with a standard deviation of 1.4 moths/trap.

The mean number is 1.2 moths/trap, but several have more.

a.

The population is the number of moths found in traps places by the agriculture departments.

The population mean μ= 1.2 moths per trap

The population standard deviation δ= 1.4 moths per trap

b.

There was a random sample of 60 traps,

The sample mean obtained is X[bar]= 1

And the sample standard deviation is S= 2.4

c.

As the text says, this variable is strongly right-skewed, if it is so, then you would expect that the data obtained from the population will also be right-skewed.

d. and e.

Because you have a sample size of 60, you can apply the Central Limit Theorem and approximate the distribution of the sampling mean to normal:

X[bar]≈N(μ;σ²/n)

The mean of the distribution is μ= 1.2

And the standard deviation is σ/√n= 1.4/50= 0.028

f. and g.

Normally the distribution of the sample mean has the same shape of the distribution of the original study variable. If the sample size is large enough, as a rule, a sample of size greater than or equal to 30 is considered sufficient you can apply the theorem and approximate the distribution of the sample mean to normal.

You have a sample size of n=10 so it is most likely that the sample mean will have a right-skewed distribution as the study variable. The sample size is too small to use the Central Limit Theorem, that is why you cannot use the Z table to calculate the asked probability.

I hope it helps!

6 0

3 years ago

A researchers wants to determine the mean weight of avocados grown in Southern California. The population from which the sample

natka813 [3]

Answer: (0.465, 5.535)

Step-by-step explanation:

Formula to calculate the confidence interval (<em>when population standard deviation is unknown</em>) is given by :-

$\overline{x}\pm t_{\alpha/2} \dfrac{s}{\sqrt{n}}$

, where $\overline{x}$ = sample mean.

s= sample standard deviation.

n= Sample size.

$t_{\alpha/2}$ = critical value

By considering the given information , we have

$\overline{x}=6$

s=0.75

n= 9

Significance level = $\alpha=0.1$ [1-0.90=0.1]

By using students' t distribution -table , the critical value for 95% confidence level :

$t_{\alpha/2 , n-1}=t_{0.1/2,\ 8}=1.86$

[Note: degree of freedom = n-1]

Now, the 90% confidence interval for the true mean weight of these Southern California avocados will be :

$6\pm (1.86) \dfrac{0.75}{\sqrt{9}}$

$6\pm (1.86) \dfrac{0.75}{3}$

$6\pm (1.86) 0.25$

$6\pm 0.465=(6-0.465,\ 6+0.465)=(0.465,\ 5.535)$

Hence, the required confidence interval =(0.465, 5.535)

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3 years ago

Fill in the blank with >,<, or = : 4.82 ___ 6.1

masya89 [10]

> is the answer. greater than

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What expressions are equivalent to -3.75 +2 (-4x+6.1) -3.25x

Oksana_A [137]

-3.75-8x+12.2-3.25x
-7x+8x+12.2
1×+12.2

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3 years ago