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1 year ago

5

Solve for x

ac{3-5x}{5}" alt="-7 \geq \frac{3-5x}{5}" align="absmiddle" class="latex-formula">

1 answer:

Levart [38]1 year ago

4 0

X is greater than or equal to 38/5

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The population mean annual salary for environmental compliance specialists is about $62,000. A random sample of 32 specialists

lakkis [162]

Answer: 0.002718

Step-by-step explanation:

Given : The population mean annual salary for environmental compliance specialists is about $62,000.

i.e. $\mu=62000$

Sample size : n= 32

$\sigma=6200$

Let x be the random variable that represents the annual salary for environmental compliance specialists.

Using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$ , the z-value corresponds to x= 59000 will be :

$z=\dfrac{59000-62000}{\dfrac{6200}{\sqrt{32}}}\approx\dfrac{-3000}{\dfrac{6200}{5.6568}}=-2.73716129032\approx-2.78$

Now, by using the standard normal z-table , the probability that the mean salary of the sample is less than $59,000 :-

$P(z$

Hence, the probability that the mean salary of the sample is less than $59,000= 0.002718

3 0

2 years ago

Please help!<br> I don't know how to read/answer the image

rusak2 [61]

Answer:

SAS

Step-by-step explanation:

SSS= Side Side Side

SAS= Side Angle Side

ASA= Angle Side Angle

SAA= Side Angle Angle

HL= Height Length

7 0

2 years ago

The curve y = |x|/ 5 − x2 is called a bullet-nose curve. find an equation of the tangent line to this curve at the point (2, 2).

diamong [38]

We have the following curve:

$y=\frac{\left | x \right |}{5-x^2}$

So we need to find <span>an equation of the tangent line to this curve at the point $(2,2)$ . So let's find out if this point, in fact, belongs to the curve:

</span> $If \ x=2 \\ \\ y=\frac{\left | 2 \right |}{5-2^2}=\frac{\left | 2 \right |}{5-4}=2$ .
<span>
We also know that:

</span> $\left | x \right |= \left \{ {{x \ if \ x \ \geq 0} \atop {-x \ if \ x\ \textless \ 0}} \right.$ <span>

Given that the point is:

</span> $(2,2)\ that \ is: \\ x=2\ \textgreater \ 0$

Then we will say that:

$\left | x \right |=x$

Therefore:

$y=\frac{x}{5-x^2}$

Computing the derivative:

$y=\frac{x}{5-x^2} \\ \frac{dy}{dx}= \frac{(1)(5-x^2)-(-2x)x}{(5-x^2)^2}=\frac{5+x^2}{(5-x^2)^2}$

So the derivative solved for $x=2$ is in fact the slope of the line at the point $(2,2)$ , then:

$\frac{dy}{dx} |_{x=2}=\frac{5+x^2}{(5-x^2)^2}|_{x=2}=\frac{5+2^2}{(5-2^2)^2}=9 \\ \\ \therefore m=\frac{dy}{dx} |_{x=2}=9$

Finally, the tangent line is:

$y-y_1=m(x-x_1) \\ \therefore y-2=9(x-2) \\ \therefore \boxed{y=9x-16}$

<em>This is shown in the figure below.</em><span>
</span>

8 0

2 years ago

Which correctly describes a cross section of the right rectangular prism if the base is a rectangle measuring 15 inches by 8 inc

almond37 [142]

Answer:

The 3 correct answers are 1, 3, and 5:

(Correct) A cross section parallel to the base is a rectangle measuring 15 inches by 8 inches.

(Wrong) A cross section parallel to the base is a rectangle measuring 15 inches by 6 inches.

(Correct) A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 6 inches by 15 inches.

(Wrong) A cross section perpendicular to the base through the midpoints of the 8-inch sides is a rectangle measuring 4 inches by 15 inches.

(Correct) A cross section not parallel to the base that passes through opposite 6-inch edges is a rectangle measuring 6 inches by greater than 15 inches.

7 0

2 years ago

Read 2 more answers

Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7<br> how do i solve this

DIA [1.3K]

Answer:

<em>Solution: x=5, y=4</em>

Step-by-step explanation:

<u>System of Equations</u>

We need to solve:

- 5x + 9y = 11

x - 3y = - 7

There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:

x = - 7 + 3y

Now replace it into the first equation:

- 5(- 7 + 3y) + 9y = 11

Operate:

35 - 15y + 9y = 11

Simplify:

35 - 6y = 11

Rearrange:

- 6y = 11 - 35 = -24

Solve:

y = -24 / -6

y = 4

Finally, since

x = - 7 + 3y

x = - 7 + 3*4

x = - 7 + 12

x = 5

Solution: x=5, y=4

3 0

2 years ago