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2 years ago

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Sal wrote the statement below to represent the inequality 8 n minus 5 less-than 25. Which words should Sal use to complete the v

erbal statement? The product of 8 and n decreased by 5 is ___________

2 answers:

devlian [24]2 years ago

7 0

Answer:

A.less than

Step-by-step explanation:

i took the test on edg.Hope it helps =)

HACTEHA [7]2 years ago

3 0

Answer:

The product of 8 and n decreased by 5 is less than 25

Step-by-step explanation:

An inequality is used to compare two values, showing that one value smaller than, larger than, or not equal to another value. x ≠ y means that x is not equal to y. x < y means that x is less than y and x > y means that x is greater than y.

The inequality 8n - 5 < 25 can be written in statement as the product of 8 and n decreased by 5 is less than 25.

The product of 8 and n (means 8n) decreased by 5 (means 8n - 5) is less than 25 (means 8n - 25 < 25)

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A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the number

serg [7]

Answer:

The probability distribution is

X : 0 1 2

f(X) : 2/7 4/7 1/7

Step-by-step explanation:

Let x is the number of defective sets purchased by the hotel.

Total number of television sets = 7

Total number of defective television sets = 2

Since there are 2 defective television sets and hotel purchase 3 sets, So, X=0,1,2.

If X=0,

$P(X=0)=\frac{^5C_3}{^7C_3}=\frac{10}{35}=\frac{2}{7}$

If X=1,

$P(X=1)=\frac{^5C_2\cdot ^2C_1}{^7C_3}=\frac{10\cdot 2}{35}=\frac{4}{7}$

If X=2,

$P(X=2)=\frac{^5C_1\cdot ^2C_2}{^7C_3}=\frac{5\cdot 1}{35}=\frac{1}{7}$

The probability distribution is

X : 0 1 2

f(X) : 2/7 4/7 1/7

The probability histogram is shown below.

3 0

2 years ago

Use lagrange multipliers to find the points on the given surface that are closest to the origin. y2 = 64 + xz

Inessa [10]

The distance between an arbitrary point on the surface and the origin is

$d(x,y,z)=\sqrt{x^2+y^2+z^2}$

Recall that for differentiable functions $g(x)$ and $h(x)$ , the composition $g(h(x))$ attains extrema at the same points that $h(x)$ does, so we can consider an augmented distance function

$D(x,y,z)=x^2+y^2+z^2$

The Lagrangian would then be

$L(x,y,z,\lambda)=x^2+y^2+z^2+\lambda(y^2-64-xz)$

We have partial derivatives

$\begin{cases}L_x=2x-\lambda z\\L_y=2y+2y\lambda\\L_z=2z-\lambda x\\L_\lambda=y^2-64-xz\end{cases}$

Set each partial derivative to 0 and solve the system to find the critical points.

From the second equation it follows that either $y=0$ or $\lambda=-1$ . In the first case we arrive at a contradiction (I'll leave establishing that to you). If $\lambda=-1$ , then we have

$\begin{cases}2x+z=0\\2z+x=0\end{cases}\implies x=0,z=0$

This means $y^2=64\implies y=\pm8$

so that the points on the surface closest to the origin are $(0,\pm8,0)$ .

8 0

2 years ago

How does the saying "money breeds money" apply to simple interest?

r-ruslan [8.4K]

It applies because interest slowly increases the amount of money gained. IF you have any Tolkien related questions, feel free to ask me

6 0

2 years ago

Read 2 more answers

On average, the number of customers who had items to return for refunds or exchanges at a certain retail store's service desk is

spayn [35]

Answer:

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

Step-by-step explanation:

With the weekly average we can estimate the daily average for customers, assuming 7 days a week:

$M=756/7=108$

We can model this situation with a Poisson distribution, with parameter λ=108. But because the number of events is large, we use the normal aproximation:

$P(\lambda)\approx N(\lambda,\lambda)$

Then we can calculate the z value for x=100:

$z=\frac{x-\mu}{\sigma}=\frac{100-108}{\sqrt{108}}=\frac{-8}{10.4} =-0.77$

Now we calculate the probability of x>100 as:

$P(x>100)=P(z>-0.77)=0.78$

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

5 0

2 years ago

A sinusoidal function whose period is π/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3. What is the equ

Eddi Din [679]

Answer:

$f(\theta)=3+7sin(4\theta)$

Step-by-step explanation:

The sinusoidal function has a general form of:

$f(\theta)=Y+Asin(k\theta)$

The period is given by:

$P=\frac{2\pi}{k}\\\frac{\pi}{2}= \frac{2\pi}{k}\\k=4$

Y is the y-intercept, thus y = 3.

At the maximum value:

$f(max) = Y+A\\10 = 3+A\\A=7$

At the minimum value:

$f(min) = Y-A\\-4 = 3-A\\A=7$

Therefore, the equation of the function described is:

$f(\theta)=3+7sin(4\theta)$

6 0

2 years ago