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3 years ago

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A 50-foot ladder leans against a wall, as shown in the figure below. If the base of the ladder is 30 feet away from the wall, ho

w tall is the wall?
Select one:
A. 3
B. 4
C. 5
D. 40

1 answer:

tamaranim1 [39]3 years ago

4 0

Pythagorean theorem gives u answer d. Ill include work for you in chat

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What is the domain (in interval notation) of the following functions?

alexgriva [62]

$1.\\g(x)=\frac{3}{5x-4}\\\\D:5x-4\neq0\to5x\neq4\ \ \ /:5\to x\neq\frac{4}{5}\to x\in\mathbb{R}\ \backslash\ \{\frac{4}{5}\}\\\\2.\\h(x)=\frac{\sqrt{x}}{x-5}\\\\D:x\geq0\ \wedge\ x-5\neq0\to x\geq0\ \wedge\ x\neq5\to x\in\left$

$3.\\f(x)=\frac{\sqrt{x}}{x^2-5x}\\\\D:x\geq0\ \wedge\ x^2-5x\neq0\to x\geq0\ \wedge\ x(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq0\ \wedge\ x\neq5\to x\in\mathbb{R^+}\ \backslash\ \{5\}\\\\4.\\g(x)=\frac{\sqrt{x}+5}{x^2-x-20}\\\\D:x\geq0\ \wedge\ x^2-x-20\neq0\to x\geq0\ \wedge\ (x+4)(x-5)\neq0\\\\\to x\geq0\ \wedge\ x\neq-4\ \wedge\ x\neq5\to x\in\left$

$5.\\h(x)=\frac{3}{x^2+1}\\\\D:x^2+1\neq0\to x^2\neq-1\to x\in\mathbb{R}\\\\6.\\f(x)=\frac{\sqrt{x-2}}{x+1}\\\\D:x-2\geq0\ \wedge\ x+1\neq0\to x\geq2\ \wedge\ x\neq-1\to x\in\left$

$7.\\g(x)=\frac{x^2}{3x^2-x-2}\\\\D:3x^2-x-2\neq0\to (3x+2)(x-1)\neq0\to x\neq-\frac{2}{3}\ \wedge\ x\neq1\\\\\to x\in\mathbb{R}\ \backslash\ \{-\frac{2}{3};\ 1\}\\\\8.\\h(x)=3(x-4)^2-7\\\\D:x\in\mathbb{R}$

4 0

2 years ago

Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

Aleks04 [339]

Answer:

a) $\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) $P(\bar X \leq 77)=P(Z$

d) See figure attached

Step-by-step explanation:

Previous concepts

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

$E(X) = 75$

$sd(X) = 7$

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X \leq 77)=P(Z$

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

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2 years ago

The volume of a prism changes from 20 to 540 after a dilation. what was the scale factor of the dilation?

lyudmila [28]

Scale factor is used by architects or engineers to transfer their prototype idea to large-scale use. If the volume of a prism is 20, you need to multiply its dimensions with a scale factor to find the new volume which is 540. For example, if the volume is doubled, this means you used a scale factor of 2. Hence, you just have to divide the new volume by the smaller volume.

Scale factor = 540/20
Scale factor = 27

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3 years ago

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Solve x divided by four equals eight . (1 point)<br><br><br> 4<br> −4<br> 32<br> −32

schepotkina [342]

X/4 = 8
multiply both sides by 4 to get the value of x
x=32

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2 years ago

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If a radius of a circle is 12 feet, what is the area and perimeter of the circle?

Vesna [10]

Area of a circle=πr²
area of this cirlce=π*(12 ft)²=144π ft²≈452.39 ft².

answer 1= the area of this circle is 452.39 ft².

Perimeter of a circle=2πr.
Perimeter of this cirlce=2π(12 ft)=24π ft≈75.4 ft

<span>answer 2= the perimeter of this cirlce is 75.4 ft.</span>

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2 years ago

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