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3 years ago

What height on the wall will a 15 foot ladder reach if it is placed 3.5 feet from the base of the wall...???

Mathematics

2 answers:

umka2103 [35]3 years ago

7 0

Answer:

14.6 feet

Step-by-step explanation:

Let the height of the ladder be the hypotenuse, the distance from the wall be the base and the height till the ladder reaches be the perpendicular.

Using Pythogoras theorem,

H^2 = p^2+b^2

p^2 = H^2-b^2

p = under root(H^2-b^2)

p = under root(225 - 12.25)

p = 14.6 feet

Amiraneli [1.4K]3 years ago

7 0

14.6

hope this helps have a blessed day

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Akimi4 [234]

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3 years ago

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Concerns about the climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g. from r

natta225 [31]

Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

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 normal distributions can be 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.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that $n = 34$

We have that $\mu = 0.937, \sigma = 0.009$

By the Central Limit Theorem, $s = \frac{0.009}{\sqrt{34}} = 0.0015$

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

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

By the Central Limit Theorem

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

$-2.575 = \frac{X - 0.937}{0.0015}$

$X - 0.937 = -2.575*0.0015$

$X = 0.933$

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

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

$2.575 = \frac{X - 0.937}{0.0015}$

$X - 0.937 = 2.575*0.0015$

$X = 0.941$

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

6 0

3 years ago

How do you Solve d+7/−3=4?

vova2212 [387]

Answer:

One solution was found :

d = 19/3 = 6.333

Step-by-step explanation:

Step by step solution :

Step 1 :

Simplify ——

-3

Equation at the end of step 1 :

(d + ——) - 4 = 0

-3

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using -3 as the denominator :

d d • -3

d = — = ——————

1 -3

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:

d • 3 + 7 • -1 3d - 7

—————————————— = ——————

3 3

Equation at the end of step 2 :

(3d - 7)

———————— - 4 = 0

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

4 4 • 3

4 = — = —————

1 3

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(3d-7) - (4 • 3) 3d - 19

———————————————— = ———————

3 3

Equation at the end of step 3 :

3d - 19

——————— = 0

Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...

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

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

3d-19

————— • 3 = 0 • 3

Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

3d-19 = 0

Solving a Single Variable Equation :

4.2 Solve : 3d-19 = 0

Add 19 to both sides of the equation :

3d = 19

Divide both sides of the equation by 3:

d = 19/3 = 6.333

One solution was found :

d = 19/3 = 6.333

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3 years ago

3. Given the same sample statistics, which level of confidence would produce

Irina-Kira [14]

Answer:

99%, because as the level of confidence increases, Zc increases.

Step-by-step explanation:

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3 years ago

Pls help pls pls ): precalc

Lena [83]

<h3>Answer: Choice A</h3>

$\log_p N = b$ is not the same as $b^p = N$

The base of the log is p, while the base of the exponential is b. The two don't match. If it said $\log_p N = b \text{ is the same as } p^b = N$ then it would be a valid statement since the bases are both p.

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Extra info:

Choice B is a valid statement because Ln is a natural log with base 'e'

Choice C is valid as any square root is really something to the 1/2 power

Choice D is valid for similar reasons mentioned earlier

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3 years ago

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